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A semilinear parabolic system in a bounded domain

Authors:

Institution:

1. Departamento de Matemáticas, Facultad de Ciencias, Univ. del Pais Vasco, Apartado 644, 48080, Bilbao, Spain
2. Dpto. Matemática Aplicada, Facultad de Matemáticas, Univ. Complutense, 28040, Madrid, Spain

Abstract:

Consider the system

$\left\{ \begin{gathered} u_t - \Delta u = v^p , in Q = \{ (t, x), t > 0, x \in \Omega \} , \hfill \\ v_t - \Delta v = u^q , in Q , \hfill \\ u(0, x) = u_0 (x) v(0, x) = v_0 (x) in \Omega , \hfill \\ u(t, x) = v(t, x) = 0 , when t \geqslant 0, x \in \partial \Omega , \hfill \\ \end{gathered} \right.$

Keywords:
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