Uniqueness for an elliptic-parabolic problem with Neumann boundary condition

Boris P. Andreianov () and Fouzia Bouhsiss ()
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Boris P. Andreianov: Université de Provence, Centre de Mathématiques et Informatique
Fouzia Bouhsiss: Université de Franche-Comte, Laboratoire de Mathématiques

A chapter in Nonlinear Evolution Equations and Related Topics, 2004, pp S273-S295 from Springer

Abstract: Abstract We consider the problem $$ b\left( u \right) - \Delta u + div F\left( u \right) = f$$ in a smooth bounded domain $$ \Omega \subset {\mathbb{R}^N}$$ , as well as the corresponding evolution equation $$ b{\left( u \right)_t} - \Delta u + div F\left( u \right) = f$$ , $$ b\left( {u\left( {0,.} \right)} \right) = {b^0}.$$ . For the stationary equation we show existence results, then we adapt the techniques of doubling of variables to the case of the homogeneous Neumann boundary conditions and obtain the appropriate L 1-contraction principle and uniqueness. Subsequently, we are able to apply the nonlinear semigroup theory and prove the L 1 -contraction principle for the associated evolution equation.

Keywords: 35J65; 35K60; 35K65; 47H06; 47H20; Degenerate parabolic equations; Neumann boundary condition; doubling of variables; nonlinear semigroup theory (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_37

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DOI: 10.1007/978-3-0348-7924-8_37

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