Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type (Hardcover)

Samuil D. Eidelman

ISBN 10: 3764371153 / ISBN 13: 9783764371159

Editore: Birkhauser Verlag AG, Basel, 2004

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Hardcover. The theory of parabolic equations, a well-developed part of the contemporary theory of partial differential equations and mathematical physics, is the subject of immense research activity. A stable interest to parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in applied problems of natural science, technology, and economics.This book aims at a consistent and, as far as possible, complete exposition of analytic methods of constructing, investigating, and using fundamental solutions of the Cauchy problem for the following four classes of linear parabolic equations: - 2b-parabolic partial differential equations, in which every spatial variable may have its own weight with respect to the time variable - degenerate partial differential equations of Kolmogorov's structure, which generalize classical Kolmogorov equations of diffusion with inertia- pseudo-differential equations with non-smooth quasi-homogeneous symbols- fractional diffusion equations.All of these provide mathematical models for various diffusion phenomena.In spite of a large number of research papers on the subject, this is the first book devoted to this topic. It will be useful both for mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes. The theory of parabolic equations, a well-developed part of the contemporary partial differential equations and mathematical physics, is the subject theory of of an immense research activity. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9783764371159

Dati bibliografici

• Titolo: Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type (Hardcover)
• Editore: Birkhauser Verlag AG, Basel
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 3764371153
• ISBN 13: 9783764371159
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

This book is devoted to new classes of parabolic differential and pseudo-differential equations extensively studied in the last decades, such as parabolic systems of a quasi-homogeneous structure, degenerate equations of the Kolmogorov type, pseudo-differential parabolic equations, and fractional diffusion equations. It will appeal to mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes.

Contenuti

1 Equations. Problems. Results. Methods. Examples.- 1.1 Differential equations.- 1.2 Pseudo-differential equations.- 1.3 Main lemmas.- 2 Parabolic Equations of a Quasi-Homogeneous Structure.- 2.1 Fundamental solution of the Cauchy problem for equations with bounded coefficients.- 2.2 Cauchy problem for equations with bounded coefficients.- 2.3 Equations with growing coefficients.- 2.4 Equations with degenerations on the initial hyperplane.- 2.5 Comments.- 3 Degenerate Equations of the Kolmogorov Type.- 3.1 Fundamental solution of the Cauchy problem.- 3.2 Cauchy problem.- 3.3 Properties of solutions of the Fokker-Planck-Kolmogorov equations.- 3.4 Comments.- 4 Pseudo-Differential Parabolic Equations with Quasi-Homogeneous Symbols.- 4.1 Fundamental solution of the Cauchy problem.- 4.2 Cauchy problem.- 4.3 On qualitative properties of solutions of some equations with constant symbols.- 4.4 Comments.- 5 Fractional Diffusion Equations.- 5.1 Fractional derivatives.- 5.2 Fundamental solution of the Cauchy problem.- 5.3 The Cauchy problem: Existence and representation of solutions.- 5.4 Uniqueness theorems.- 5.5 Comments.- Appendix. Fox’s H-Functions.- Notation.