Generalized motion by curvature with a Dirichlet condition
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.
scientific article; zbMATH DE number 703253