LONG-TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR REACTION DIFFUSION EQUATIONS INVOLVING L1 DATA
2012 ◽
Vol 14
(01)
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pp. 1250007
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Keyword(s):
L1 Data
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In this paper we consider the long-time behavior of solutions to nonlinear reaction diffusion equations involving L1 data, [Formula: see text] where Ω is a smooth bounded domain and u0, g ∈ L1(Ω). Using a decomposition technique combined with a bootstrap argument we establish some uniform regularity results on the solutions, by which we prove that the solution semigroup generated by the problem above possesses a global attractor [Formula: see text] in L1(Ω). Moreover, we obtain that the attractor is actually invariant, compact in [Formula: see text], q < max {N/(N-1), (2p-2)/p}, and attracts every bounded subset of L1(Ω) in the norm of [Formula: see text], 1 ≤ r < ∞.
Keyword(s):
2012 ◽
Vol 13
(3)
◽
pp. 1401-1415
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Keyword(s):
1978 ◽
Vol 35
(1)
◽
pp. 1-16
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2011 ◽
Vol 2011
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pp. 1-27
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Keyword(s):