Asymptotic Behavior of a Class of Degenerate Parabolic Equations

Asymptotic Behavior of a Class of Degenerate Parabolic Equations

and Applied Analysis 3 2.1. Functional Spaces The appropriate Sobolev space for 1.1 is H 0 Ω , defined as a completion of C ∞ 0 Ω with respect to the norm

The Asymptotic Behavior of the Solutions of Degenerate Parabolic Equations

Existence of stationary states is established by means of the method of upper and lower solutions. The structure of the solution set is discussed and a uniqueness property for certain classes is proved by a generalized maximum principle. It is then shown that all solutions of the parabolic equation converge to a stationary state.

Asymptotic expansions for degenerate parabolic equations

Article history: Received 14 May 2014 Accepted after revision 26 September 2014 Available online 11 October 2014 Presented by Olivier Pironneau We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the unifo...

On a class of degenerate parabolic equations of Kolmogorov type

We adapt the Levi’s parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.

Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations