Attractors for the semilinear reaction–diffusion equation with distribution derivatives in unbounded domains☆

Abstract In this paper, we prove the existence of global attractors for a nonlinear reaction–diffusion equation with a nonlinearity having a polynomial growth of arbitrary order p - 1 ( p ⩾ 2 ) , and with distribution derivatives in the inhomogeneous term. The global attractors are obtained in L 2 ( R n ) and L p ( R n ) , respectively. A new a priori estimate method has been used. Since the solutions of the equation have no higher regularity and the semigroup associated with the solutions is not continuous in L p ( R n ) , the results are new and appear to be optimal.

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