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Model Parabolic Problems

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

Abstract

In Chapter II, we mainly consider semilinear parabolic problems of the form
$$ \left. {\begin{array}{*{20}c} {u_t - \Delta u = f\left( u \right),{\mathbf{ }}x \in \Omega ,t > 0} \\ {u = 0,{\mathbf{ }}x \in \partial \Omega ,t > 0,} \\ {u\left( {x,0} \right) = u_0 \left( x \right),{\mathbf{ }}x \in \Omega ,} \\ \end{array} {\mathbf{ }}} \right\} $$
where f is a C1-function with a superlinear growth. For simplicity, we formulate most of our assertions for the model case f(u) = |u|p-1u with p 1, but the methods of our proofs can be applied to more general parabolic problems (not necessarily of the form (14.1)). Some of possible generalizations and modifications will be mentioned as remarks, other can be found in the subsequent chapters.

Keywords

Classical Solution Global Existence Comparison Principle Universal Bound Threshold Solution 
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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