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Equations with Gradient Terms

Part of the Birkhäuser Advanced Texts / Basler Lehrbücher book series (BAT)

Abstract

In Chapter IV, we consider problems with nonlinearities depending on u and its space derivatives:
$$ \left. {\begin{array}{*{20}c} {u_t - \Delta u = F\left( {u,\nabla u} \right),{\mathbf{ }}x \in \Omega ,t > 0,} \\ {u = 0,{\mathbf{ }}x \in \partial \Omega ,t > 0,} \\ {u\left( {x,0} \right) = u_0 \left( x \right),{\mathbf{ }}x \in \Omega .} \\ \end{array} {\mathbf{ }}} \right\} $$
Here F = F(u, ξ):ℝ×ℝn → lo is a C1-function (except for problem (34.4) with 1 < q > 2, see below).

Keywords

Maximum Principle Global Solution Model Problem Global Existence Comparison Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2007

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