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

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.