On a semilinear parabolic system of reaction–diffusion with absorption
Marie‐Françoise Bidaut‐Véron, Marta García‐Huidobro, Cecilia S. Yarur · Asymptotic Analysis · 2003
We consider the semilinear parabolic system with absorption terms in a bounded domain Ω of $\mathbb{R}^{N}$ [Formula: see text] where p,q>0 and k,ℓ≥0, with Dirichlet or Neuman conditions on $\curpartial\varOmega\times(0,\infty)$ . We study the existence and uniqueness of the Cauchy problem when the initial data are L 1 functions or bounded measures. We find invariant regions when u 0 , v 0 are nonnegative, and give sufficient conditions for positivity or extinction in finite time.