Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type (Operator Theory: Advances and Applications, 152)

Eidelman, Samuil D., Ivasyshen, Stepan D., Kochubei, Anatoly N.

ISBN 10: 3764371153 / ISBN 13: 9783764371159

Editore: Birkhäuser, 2004

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Dati bibliografici

• Titolo: Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type (Operator Theory: Advances and Applications, 152)
• Editore: Birkhäuser
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 3764371153
• ISBN 13: 9783764371159
• Rilegatura: Rilegato
• 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.