Attractors for non-autonomous parabolic problems with singular initial data

Attractors for non-autonomous parabolic problems with singular initial data

Article history: Received 7 May 2010 Revised 3 May 2011 Available online 17 May 2011

Attractors for Parabolic Equations with Nonlinear Boundary Conditions, Critical Exponents, and Singular Initial Data

Hölder-estimates for non-autonomous parabolic problems with rough data

In this paper we establish Hölder estimates for solutions to non-autonomous parabolic equations on non-smooth domains which are complemented with mixed boundary conditions. The corresponding elliptic operators are of divergence type, the coefficient matrix of which depends only measurably on time. These results are in the tradition of the classical book of Ladyshenskaya et al. [39], which also ...

Pullback Attractors for Non-autonomous Parabolic Equations Involving Grushin Operators

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusi...

Uniform Attractors for the Non–autonomous Parabolic Equation with Nonlinear Laplacian Principal Part in Unbounded Domain

In this paper, we are concerned with the asymptotic behavior of the solution for the non-autonomous parabolic equation with nonlinear Laplacian principal part in R n. The existence of the (L2(Rn),L2(Rn)) -uniform attractor, the (L2(Rn),Lp(Rn)) -uniform attractor and the (L2(Rn),W 1,p(Rn)∩Lq(Rn)) -uniform attractor will be proved. Mathematics subject classification (2010): 35B40, 35B41, 35L70.