Abstract
We give a sufficient condition for the existence of a Lyapunov function for the system $$\eqalign{ a_t&=\nabla(k(a,c)\nabla a-h(a,c)\nabla c),\quad\ x\in{\mit\Omega} ,\ t>0,\cr \varepsilon c_t&=k_c{\mit\Delta} c-f(c)c+g(a,c),\quad\ x\in{\mit\Omega} ,\ t>0
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