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

Softcover Nachdruck of the original 1. Auflage 2004
ISBN: 978-3-0348-9592-7
Verlag: Birkhäuser Basel

Buch, Englisch, Band 152, 390 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 610 g

Reihe: Operator Theory: Advances and Applications

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 four important classes of linear parabolic equations.
It will be useful both for mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes.

Zielgruppe

Research

Autoren/Hrsg.

Eidelman, Samuil D.

Kochubei, Anatoly N.

Ivasyshen, Stepan D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.