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Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction-diffusion equations. (English) Zbl 1126.37049

Summary: We introduce the concept of norm-to-weak continuous process in a Banach space, and obtain the existence of pullback attractors for this kind of process. Then we give a new method for proving the existence of the pullback attractors. As an application, we obtain the existence of pullback attractors for nonautonomous reaction-diffusion equation in \(H^{1}_{0}\) with exponential growth of the external force.

MSC:

37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
34D45 Attractors of solutions to ordinary differential equations
35B41 Attractors
35K57 Reaction-diffusion equations
37B25 Stability of topological dynamical systems
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