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Generalized motion by curvature with a Dirichlet condition. (English) Zbl 0810.35048
The authors study existence, uniqueness and large time behaviour of the solution of the following problem \[ u_ t= |\nabla u| \text{ div} \Biggl( {{\nabla u} \over {|\nabla u|}} \Biggr), \quad u(x,t)= h(x) \text{ for } x\in \partial\Omega, \quad u(x,0)= g(x) \text{ for } x\in\Omega, \] where \(\Omega\subset \mathbb{R}^ n\) is a bounded domain and \(g\) and \(h\) are given data.

MSC:
35K65 Degenerate parabolic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
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