Existence results for a fourth order partial differential equation arising in condensed matter physics

Title:

Existence results for a fourth order partial differential equation arising in condensed matter physics

Creator:

Escudero, Carlos, Gazzola, Filippo, Hakl, Robert, Peral, Ireneo, and Torres, Pedro José

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b8eefde1-4ba6-47ec-b89d-137b66c0d53c
uuid:b8eefde1-4ba6-47ec-b89d-137b66c0d53c
doi:10.21136/MB.2015.144457

Subject:

higher order parabolic equation, existence of solution, blow-up in finite time, higher order elliptic equation, variational method, and strongly singular boundary value problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

385-393

Source:

Mathematica bohemica | 2015 Volume:140 | Number:4

Harvested from:

CDK

Metadata only:

false