Christodoulou, Demetrios 1951
Overview
Works:  48 works in 145 publications in 4 languages and 2,893 library holdings 

Genres:  History Masses Conference papers and proceedings 
Roles:  Author, Thesis advisor, Other 
Publication Timeline
.
Most widely held works about
Demetrios Christodoulou
Most widely held works by
Demetrios Christodoulou
The Global Nonlinear Stability of the Minkowski Space (PMS41) by
Demetrios Christodoulou(
)
3 editions published between 1994 and 2016 in English and held by 818 WorldCat member libraries worldwide
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski spacetime. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski spacetime. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski spacetime, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of
3 editions published between 1994 and 2016 in English and held by 818 WorldCat member libraries worldwide
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski spacetime. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski spacetime. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski spacetime, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of
The formation of black holes in general relativity by
Demetrios Christodoulou(
)
16 editions published between 2008 and 2009 in English and held by 650 WorldCat member libraries worldwide
In 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity. A major challenge since that time has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. The present monograph achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves. The theorems proved in the present monograph constitute the first foray into the longtime dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of EulerLagrange equations of hyperbolic type, and provides the means to tackle problems which have hitherto seemed unapproachable. This monograph will be of interest to people working in general relativity, geometric analysis, and partial differential equations
16 editions published between 2008 and 2009 in English and held by 650 WorldCat member libraries worldwide
In 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity. A major challenge since that time has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. The present monograph achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves. The theorems proved in the present monograph constitute the first foray into the longtime dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of EulerLagrange equations of hyperbolic type, and provides the means to tackle problems which have hitherto seemed unapproachable. This monograph will be of interest to people working in general relativity, geometric analysis, and partial differential equations
The action principle and partial differential equations by
Demetrios Christodoulou(
Book
)
11 editions published between 2000 and 2016 in English and held by 548 WorldCat member libraries worldwide
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and HamiltonJacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the EulerLagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domainofdependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media
11 editions published between 2000 and 2016 in English and held by 548 WorldCat member libraries worldwide
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and HamiltonJacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the EulerLagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domainofdependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media
The global nonlinear stability of the Minkowski space by
Demetrios Christodoulou(
Book
)
15 editions published between 1989 and 2014 in English and held by 340 WorldCat member libraries worldwide
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski spacetime. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski spacetime. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski spacetime, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation
15 editions published between 1989 and 2014 in English and held by 340 WorldCat member libraries worldwide
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski spacetime. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski spacetime. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski spacetime, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation
Mathematical problems of general relativity I by
Demetrios Christodoulou(
Book
)
18 editions published between 2005 and 2008 in English and held by 206 WorldCat member libraries worldwide
"The domain of application of Einstein's general relativity theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This book is intended for advanced students and researchers seeking an introduction into the methods and applications of general relativity."Jacket
18 editions published between 2005 and 2008 in English and held by 206 WorldCat member libraries worldwide
"The domain of application of Einstein's general relativity theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This book is intended for advanced students and researchers seeking an introduction into the methods and applications of general relativity."Jacket
The formation of shocks in 3dimensional fluids by
Demetrios Christodoulou(
Book
)
10 editions published in 2007 in English and held by 177 WorldCat member libraries worldwide
The equations describing the motion of a perfect fluid were first formulated by Euler in 1752. These equations were among the first partial differential equations to be written down, but, after a lapse of two and a half centuries, we are still far from adequately understanding the observed phenomena which are supposed to lie within their domain of validity. These phenomena include the formation and evolution of shocks in compressible fluids, the subject of the present monograph. The first work on shock formation was done by Riemann in 1858. However, his analysis was limited to the simplified case of one space dimension. Since then, several deep physical insights have been attained and new methods of mathematical analysis invented. Nevertheless, the theory of the formation and evolution of shocks in real threedimensional fluids has remained up to this day fundamentally incomplete. This monograph considers the relativistic Euler equations in three space dimensions for a perfect fluid with an arbitrary equation of state. We consider initial data for these equations which outside a sphere coincide with the data corresponding to a constant state. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems that give a complete description of the maximal classical development. In particular, it is shown that the boundary of the domain of the maximal classical development has a singular part where the inverse density of the wave fronts vanishes, signalling shock formation. The theorems give a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there. A complete picture of shock formation in threedimensional fluids is thereby obtained. The approach is geometric, the central concept being that of the acoustical spacetime manifold. The monograph will be of interest to people working in partial differential equations in
10 editions published in 2007 in English and held by 177 WorldCat member libraries worldwide
The equations describing the motion of a perfect fluid were first formulated by Euler in 1752. These equations were among the first partial differential equations to be written down, but, after a lapse of two and a half centuries, we are still far from adequately understanding the observed phenomena which are supposed to lie within their domain of validity. These phenomena include the formation and evolution of shocks in compressible fluids, the subject of the present monograph. The first work on shock formation was done by Riemann in 1858. However, his analysis was limited to the simplified case of one space dimension. Since then, several deep physical insights have been attained and new methods of mathematical analysis invented. Nevertheless, the theory of the formation and evolution of shocks in real threedimensional fluids has remained up to this day fundamentally incomplete. This monograph considers the relativistic Euler equations in three space dimensions for a perfect fluid with an arbitrary equation of state. We consider initial data for these equations which outside a sphere coincide with the data corresponding to a constant state. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems that give a complete description of the maximal classical development. In particular, it is shown that the boundary of the domain of the maximal classical development has a singular part where the inverse density of the wave fronts vanishes, signalling shock formation. The theorems give a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there. A complete picture of shock formation in threedimensional fluids is thereby obtained. The approach is geometric, the central concept being that of the acoustical spacetime manifold. The monograph will be of interest to people working in partial differential equations in
Compressible flow and Euler's equations by
Demetrios Christodoulou(
Book
)
7 editions published in 2014 in English and Chinese and held by 41 WorldCat member libraries worldwide
This monograph considers the classical compressible Euler Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, the authors establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the density of the wave fronts blows up and shocks form. The authors obtain a detailed description of the geometry of this singular boundary, and a detailed analysis of the behavior of the solution there. The approach is geometric, the central concept being that of the acoustical spacetime manifold. Compared to a previous monograph treating the relativistic fluids by the first author, the present monograph not only gives simpler and selfcontained proofs but also sharpens some of the results. In addition, it explains in depth the ideas on which the approach is based. Moreover, certain geometric aspects which pertain only to the nonrelativistic theory are discussed. Compressible Flow and Euler's Equations will be of interest to scholars working in partial differential equations in general and in fluid mechanics in particular
7 editions published in 2014 in English and Chinese and held by 41 WorldCat member libraries worldwide
This monograph considers the classical compressible Euler Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, the authors establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the density of the wave fronts blows up and shocks form. The authors obtain a detailed description of the geometry of this singular boundary, and a detailed analysis of the behavior of the solution there. The approach is geometric, the central concept being that of the acoustical spacetime manifold. Compared to a previous monograph treating the relativistic fluids by the first author, the present monograph not only gives simpler and selfcontained proofs but also sharpens some of the results. In addition, it explains in depth the ideas on which the approach is based. Moreover, certain geometric aspects which pertain only to the nonrelativistic theory are discussed. Compressible Flow and Euler's Equations will be of interest to scholars working in partial differential equations in general and in fluid mechanics in particular
The Action Principle and Partial Differential Equations. (AM146) by
Demetrios Christodoulou(
)
2 editions published between 2000 and 2016 in English and held by 20 WorldCat member libraries worldwide
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and HamiltonJacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the EulerLagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domainofdependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media
2 editions published between 2000 and 2016 in English and held by 20 WorldCat member libraries worldwide
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and HamiltonJacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the EulerLagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domainofdependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media
Politikē oikonomia tēs metapolemikēs Helladas by
Demetrios Christodoulou(
Book
)
1 edition published in 1989 in Greek, Modern and held by 13 WorldCat member libraries worldwide
1 edition published in 1989 in Greek, Modern and held by 13 WorldCat member libraries worldwide
Convergent and asymptotic iteration methods in general relativity by
Demetrios Christodoulou(
Book
)
3 editions published in 1979 in English and German and held by 7 WorldCat member libraries worldwide
3 editions published in 1979 in English and German and held by 7 WorldCat member libraries worldwide
Cauchy data on a manifold by
Yvonne ChoquetBruhat(
Book
)
3 editions published in 1979 in English and German and held by 7 WorldCat member libraries worldwide
3 editions published in 1979 in English and German and held by 7 WorldCat member libraries worldwide
Report on Group Fellowship Study Tour on Settlement in Agriculture of Nomadic, SemiNomadic and Other Pastoral People : AlmaAta,
Kazakh S.S.R., U.S.S.R., 1529 September 1969 by
Demetrios Christodoulou(
Book
)
4 editions published in 1970 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1970 in English and held by 6 WorldCat member libraries worldwide
The Boost problem for weakly coupled quasilinear hyperbolic systems of the second order by
Demetrios Christodoulou(
Book
)
2 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
Investigations in gravitational collapse and the physics of black holes by
Demetrios Christodoulou(
)
4 editions published between 1971 and 1982 in English and held by 5 WorldCat member libraries worldwide
4 editions published between 1971 and 1982 in English and held by 5 WorldCat member libraries worldwide
Ta mathēmatika stēn archaia Alexandreia : Eukleidēs  Archimēdēs by
Demetrios Christodoulou(
Book
)
2 editions published in 2012 in Greek, Modern and held by 5 WorldCat member libraries worldwide
2 editions published in 2012 in Greek, Modern and held by 5 WorldCat member libraries worldwide
I. Some dynamical properties of Einstein spacetimes admitting a Gaussian Foliation : II. On certain foliations of the space
of Riemannian Metrics on compact 3manifolds by
Demetrios Christodoulou(
Book
)
3 editions published in 1977 in English and German and held by 3 WorldCat member libraries worldwide
3 editions published in 1977 in English and German and held by 3 WorldCat member libraries worldwide
Basic agrarian structural issues in the adjustment of African customary tenures to the needs of agricultural development by
Demetrios Christodoulou(
Book
)
2 editions published in 1966 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1966 in English and held by 3 WorldCat member libraries worldwide
Land tenure research papers : (nos 1,2 & 3) by
Demetrios Christodoulou(
Book
)
3 editions published in 1974 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1974 in English and held by 3 WorldCat member libraries worldwide
On the wave equation in curved spacetime by
Yvonne ChoquetBruhat(
Book
)
2 editions published in 1979 in German and English and held by 3 WorldCat member libraries worldwide
2 editions published in 1979 in German and English and held by 3 WorldCat member libraries worldwide
Existence of global solutions of the YangMills, Higgs and spinor field equations in 3+1 dimensions by
Yvonne ChoquetBruhat(
Book
)
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
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Africa Archimedes AstronomyAwards Award presentations Black holes (Astronomy) Black holes (Astronomy)Mathematics Cauchy problem ChinaHong Kong Cyprus Differential equations, Hyperbolic Differential equations, Partial Dynamics, Rigid Economic history Egypt Euclid Fluid mechanics Gas dynamicsMathematical models Generalized spaces General relativity (Physics) General relativity (Physics)Mathematics Gravitation Gravitational collapse Greece Hydrodynamics Iterative methods (Mathematics) Lagrange equations Land settlement Land tenure Manifolds (Mathematics) Mass (Physics) Mathematical physics Mathematics Mathematics, Ancient MathematicsAwards MedicineAwards Nomads Nonlinear theories Relativistic fluid dynamics ScienceAwards Shock waves Space and time Space and timeMathematics Stars Symplectic manifolds Wave equation
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Alternative Names
Christodoulou, D. 1951
Christodoulou, Demetrios 1951
Christodoulou, Dimitrios 1951
Christodoulou, Dimitris 1951
Christodulu, D. 1951
Christodulu, Dēmētrēs 1951
Christodulu, Dēmētrios 1951
Christodulu, Dēmētrios Ch. 1951
Demetrios Christodoulou Amerikaans wiskundige
Demetrios Christodoulou amerikansk fysikar og matematikar
Demetrios Christodoulou amerikansk fysiker och matematiker
Demetrios Christodoulou amerikansk fysiker og matematiker
Demetrios Christodoulou greckoamerykański matematyk i fizyk
Demetrios Christodoulou griechischUSamerikanischer Mathematiker und Physiker
Demetrios Christodoulou matematico e fisico greco
Δημήτριος Χριστοδούλου
Χριστοδουλου, Δεμετριος 1951...
Димитріос Христодулу
Кристодулу, Деметриос
دمتریوس کریستودولو ریاضیدان و فیزیکدان آمریکایی
ديمتريوس كريستودولو
デメトリオス・クリストドゥールー
德梅特里奥斯·克里斯托多罗
德米特里·克理斯特德勒
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