Critical exponent for damped wave equations with nonlinear memory |
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| Authors: | Ahmad Z. Fino |
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| Affiliation: | Laboratoire de mathématiques appliquées, UMR CNRS 5142, Université de Pau et des Pays de l’Adour, 64000 Pau, France LaMA-Liban, Lebanese University, P.O. Box 37 Tripoli, Lebanon |
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| Abstract: | We consider the Cauchy problem in Rn,n≥1, for a semilinear damped wave equation with nonlinear memory. Global existence and asymptotic behavior as t→∞ of small data solutions have been established in the case when 1≤n≤3. We also derive a blow-up result under some positive data in any dimensional space. |
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| Keywords: | 35L15 35L70 35B33 34B44 |
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