Frontiers of Mathematics in China >
Global analysis of smooth solutions to a hyperbolic-parabolic coupled system
Received date: 24 Feb 2012
Accepted date: 21 Aug 2013
Published date: 01 Dec 2013
Copyright
We investigate a model arising from biology, which is a hyperbolicparabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the Hs∩L1-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L2 decay rate of the solution and the almost optimal L2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods.
Key words： Global analysis; hyperbolic-parabolic system; decay rate; convex entropy
Yinghui ZHANG , Haiying DENG , Mingbao SUN . Global analysis of smooth solutions to a hyperbolic-parabolic coupled system[J]. Frontiers of Mathematics in China, 2013 , 8(6) : 1437 -1460 . DOI: 10.1007/s11464-013-0331-9
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