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On the existence of pullback attractors for non-autonomous reaction-diffusion equations. (English) Zbl 1145.35047

Summary: We prove the existence of pullback attractors for a nonautonomous nonlinear reaction-diffusion equation with a nonlinearity having a polynomial growth of arbitrary order \(p - 1 (p \geq 2)\). The pullback attractors are obtained in \(H_0^1(\Omega)\). For this purpose, some abstract results are established by the method of measure of noncompactness.

MSC:

35B41 Attractors
35K57 Reaction-diffusion equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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