Let Ã?© be a bounded domain in a real Euclidean space. We consider the equation du(t, x)/dt = C(x)u(t, x) + âË?«Ã?© K(x, s)u(t, s)ds +\n[f(u)](t, x (t > 0; x âË?Ë? Ã?©), where C(.) and K(ââ?¹â?¦, ââ?¹â?¦) are matrix-valued functions and f(.) is a nonlinear mapping. Conditions for the\nexponential stability of the steady state are established. Our approach is based on a norm estimate for operator commutators.
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