Number of the records: 1
Existence results for a fourth order partial differential equation arising in condensed matter physics
- 1.
SYSNO ASEP 0451937 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Existence results for a fourth order partial differential equation arising in condensed matter physics Author(s) Escudero, C. (ES)
Gazzola, F. (IT)
Hakl, Robert (MU-W) RID, SAI, ORCID
Torres, P.J. (ES)Source Title Mathematica Bohemica. - : Matematický ústav AV ČR, v. v. i. - ISSN 0862-7959
Roč. 140, č. 4 (2015), s. 385-393Number of pages 9 s. Language eng - English Country CZ - Czech Republic Keywords higher order parabolic equation ; existence of solution ; blow-up in finite time Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000215965900002 EID SCOPUS 84968572898 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
Number of the records: 1