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The one-dimensional heat equation

Author: John Rozier Cannon
Publisher: Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, 1984.
Series: Encyclopedia of mathematics and its applications, v. 23.; Encyclopedia of mathematics and its applications., Section, Analysis.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: John Rozier Cannon
ISBN: 0521302439 9780521302432
OCLC Number: 12103991
Notes: Imprint and ISBN from label on title page verso. Imprint on t.p.: Reading Mass. : Addison-Wesley, Advanced Book Program, 1984.
Publication taken over by Cambridge University Press in 1984.
"Some references to the literature on £(u)=u[subscript xx]-u[subscript t]": pages 357-477.
Includes index.
Description: xxv, 483 pages : illustrations ; 25 cm.
Contents: Editor's statement; Foreword Felix E. Browder; Preface; Preliminaries; 1. Introduction; 2. The Cauchy problem; 3. The initial-value problem; 4. The initial-boundary-value problem for the quarter plane with temperature-boundary specification; 5. The initial-boundary-value problem for the quarter plane with heat-flux-boundary specification; 6. The initial-boundary-value problem for the semi-infinite strip with temperature-boundary specification and heat-flux-boundary specification; 7. The reduction of some initial-boundary-value problems for the semi-infinite strip, to integral equations: some exercises; 8. Integral equations; 9. Solutions of boundary-value problems for all times and periodic solutions; 10. Analyticity of solutions; 11. Continuous dependence upon the data for some state-estimation problems; 12. Some numerical methods for some state-estimation problems; 13. Determination of an unknown time-dependent diffusivity a(t) from overspecified data; 14. Initial- and/or boundary-value problems for gneral regions with Hoelder continuous boundaries; 15. Some properties of solutions in general domains; 16. The solution in a general region with temperature-boundary specification: the method of perron-poincare; 17. The one-phase stefan problem with temperature-boundary specification; 18. The one-phase stefan problem with flux-boundary specification: some exercises; 19. The inhomogeneous heat equation ut=uxx+f(x,t); 20. An application of the inhomogeneous heat equation: the equation ut=uxx+f(x,t,u,ux); Symbol index; Subject index.
Series Title: Encyclopedia of mathematics and its applications, v. 23.; Encyclopedia of mathematics and its applications., Section, Analysis.
Responsibility: John Rozier Cannon ; foreword by Felix E. Browder.
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