Évolution d'une interface par capillarité et diffusion de volume. I. Existence locale en temps
We develolp a new method to solve an evolution equation in a non-cylindrical domain, by reduction to an abstract evolution equation..
MSC 2010: 44A35, 44A40
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...