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An evolution problem for linear growth functionals. (English) Zbl 0811.35061

The mixed problem is considered for the equation \(u_ t = \text{div}_ x f_ p (\nabla u)\) on \(\Omega \times [0,T]\). Existence, uniqueness and comparision of solutions are treated in subspaces of \(C^ 1 (0,T,BV (\Omega))\).
Reviewer: S.Tersian (Russe)

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

Keywords:

BV spaces
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References:

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