Year: 1997
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 4 : pp. 355–368
Abstract
The asymptotic behavior of solutions of the damped p-system is known to be described by a nonlinear diffusion equation. The previous works on this topic concern either the case of small smooth data where estimates of high-order derivatives are available by energy methods or the case of special and small rough data. For large data, the existence of solutions is proved by using the method of compensated compactness. Thus the above mentioned energy estimates are not expected. However, the compensated compactness gives a very weak justification (in the mean in time) of the asymptotics. In the present paper we prove that the natural energy estimates, which does not involve derivatives, combined with this “convergence in the mean”, gives the strong convergence in L^p_{loc} space (p is finite) as expected.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1997-JPDE-5605
Journal of Partial Differential Equations, Vol. 10 (1997), Iss. 4 : pp. 355–368
Published online: 1997-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Asymptotic behavior