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

0451937 - MÚ 2016 RIV CZ eng J - Článek v odborném periodiku
Escudero, C. - Gazzola, F. - Hakl, Robert - Torres, P.J.
Existence results for a fourth order partial differential equation arising in condensed matter physics.
Mathematica Bohemica. Roč. 140, č. 4 (2015), s. 385-393. ISSN 0862-7959
Institucionální podpora: RVO:67985840
Klíčová slova: higher order parabolic equation * existence of solution * blow-up in finite time
Kód oboru RIV: BA - Obecná matematika
http://hdl.handle.net/10338.dmlcz/144457

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.
Trvalý link: http://hdl.handle.net/11104/0252999