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Doubly nonlinear parabolic-type equations as dynamical systems. (English) Zbl 0802.35011
Summary: We study a class of doubly nonlinear parabolic PDEs, where, in addition to some weak nonlinearities, also mild nonlinearities of porous media type are allowed inside the time derivative. In order to formulate the equations as dynamical systems, some existence and uniqueness results are proved. Then the existence of a compact attractor is shown for a class of nonlinear PDEs that include doubly nonlinear porous medium-type equations. Under stronger smoothness assumptions on the nonlinearities, the finiteness of the fractal dimension of the attractor is also obtained.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
35Q40 PDEs in connection with quantum mechanics
76S05 Flows in porous media; filtration; seepage
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