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Evolution equations in non-cylindrical domains

Piermarco Cannarsa, Giuseppe Da Prato, Jean-Paul Zolésio (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We develolp a new method to solve an evolution equation in a non-cylindrical domain, by reduction to an abstract evolution equation..

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

Carlos Escudero, Filippo Gazzola, Robert Hakl, Ireneo Peral, Pedro José Torres (2015)

Mathematica Bohemica

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...

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