On global attractor for m-Laplacian parabolic equation with local and nonlocal nonlinearity |
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Authors: | Caisheng Chen |
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Institution: | Department of Applied Mathematics, Hohai University, Nanjing 210098, PR China |
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Abstract: | In this paper, we study the long-time behavior of solutions for m-Laplacian parabolic equation in Ω×(0,∞) with the initial data u(x,0)=u0(x)∈Lq, q?1, and zero boundary condition in ∂Ω. Two cases for a(x)?a0>0 and a(x)?0 are considered. We obtain the existence and Lp estimate of global attractor A in Lp, for any p?max{1,q}. The attractor A is in fact a bounded set in if a(x)?a0>0 in Ω, and A is bounded in if a(x)?0 in Ω. |
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Keywords: | m-Laplacian parabolic equation Initial boundary value problem Local and nonlocal nonlinearity Global attractor |
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