Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms
We consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt-kΔut=f(x,Δu)+g(x,u,Du,D2u) in a bounded and smooth domain Ω in Rn, where f(x,Δu) is a given monotone in Δu nonlinearity satisfying some dissipativity and g...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/805158 |
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| author | Zhigang Pan Hong Luo Tian Ma |
| author_facet | Zhigang Pan Hong Luo Tian Ma |
| author_sort | Zhigang Pan |
| collection | DOAJ |
| description | We consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt-kΔut=f(x,Δu)+g(x,u,Du,D2u) in a bounded and smooth domain Ω in Rn, where f(x,Δu) is a given monotone in Δu nonlinearity satisfying some dissipativity and growth restrictions and g(x,u,Du,D2u) is in a sense subordinated to f(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution u∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)). |
| format | Article |
| id | doaj-art-30c83013e32e47d48129995be46dfbbd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-30c83013e32e47d48129995be46dfbbd2025-02-03T01:13:05ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/805158805158Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped TermsZhigang Pan0Hong Luo1Tian Ma2Yangtze Center of Mathematics, Sichuan University, Chengdu, Sichuan 610041, ChinaCollege of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, ChinaYangtze Center of Mathematics, Sichuan University, Chengdu, Sichuan 610041, ChinaWe consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt-kΔut=f(x,Δu)+g(x,u,Du,D2u) in a bounded and smooth domain Ω in Rn, where f(x,Δu) is a given monotone in Δu nonlinearity satisfying some dissipativity and growth restrictions and g(x,u,Du,D2u) is in a sense subordinated to f(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution u∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).http://dx.doi.org/10.1155/2012/805158 |
| spellingShingle | Zhigang Pan Hong Luo Tian Ma Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms Journal of Applied Mathematics |
| title | Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms |
| title_full | Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms |
| title_fullStr | Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms |
| title_full_unstemmed | Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms |
| title_short | Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms |
| title_sort | global existence of strong solutions to a class of fully nonlinear wave equations with strongly damped terms |
| url | http://dx.doi.org/10.1155/2012/805158 |
| work_keys_str_mv | AT zhigangpan globalexistenceofstrongsolutionstoaclassoffullynonlinearwaveequationswithstronglydampedterms AT hongluo globalexistenceofstrongsolutionstoaclassoffullynonlinearwaveequationswithstronglydampedterms AT tianma globalexistenceofstrongsolutionstoaclassoffullynonlinearwaveequationswithstronglydampedterms |