On a nonlinear degenerate evolution equation with strong damping
In this paper we consider the nonlinear degenerate evolution equation with strong damping,(*) {K(x,t)utt−Δu−Δut+F(u)=0 in Q=Ω×]0,T[u(x,0)=u0, (ku′)(x,0)=0 in Ωu(x,t)=0 on ∑=Γ×]0,T[where K is a function with K(x,t)≥0, K(x,0)=0 and F is a continuous real function satisfying(...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129200070X |
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| _version_ | 1849398511254110208 |
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| author | Jorge Ferreira Ducival Carvalho Pereira |
| author_facet | Jorge Ferreira Ducival Carvalho Pereira |
| author_sort | Jorge Ferreira |
| collection | DOAJ |
| description | In this paper we consider the nonlinear degenerate evolution equation with strong damping,(*) {K(x,t)utt−Δu−Δut+F(u)=0 in Q=Ω×]0,T[u(x,0)=u0, (ku′)(x,0)=0 in Ωu(x,t)=0 on ∑=Γ×]0,T[where K is a function with K(x,t)≥0, K(x,0)=0 and F is a continuous real function satisfying(**) sF(s)≥0, for all s∈R, Ω is a bounded domain of Rn, with smooth boundary Γ. We prove the existence of a global weak solution for (*). |
| format | Article |
| id | doaj-art-a1b6a2b2397e48dea6b003796f85396c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a1b6a2b2397e48dea6b003796f85396c2025-08-20T03:38:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115354355210.1155/S016117129200070XOn a nonlinear degenerate evolution equation with strong dampingJorge Ferreira0Ducival Carvalho Pereira1IM/UFRJ and Univ. Estadual de Maringá, Paraná, BrazilUFPA, Belém, Pará, BrazilIn this paper we consider the nonlinear degenerate evolution equation with strong damping,(*) {K(x,t)utt−Δu−Δut+F(u)=0 in Q=Ω×]0,T[u(x,0)=u0, (ku′)(x,0)=0 in Ωu(x,t)=0 on ∑=Γ×]0,T[where K is a function with K(x,t)≥0, K(x,0)=0 and F is a continuous real function satisfying(**) sF(s)≥0, for all s∈R, Ω is a bounded domain of Rn, with smooth boundary Γ. We prove the existence of a global weak solution for (*).http://dx.doi.org/10.1155/S016117129200070Xweak solutionsevolution equation with damping. |
| spellingShingle | Jorge Ferreira Ducival Carvalho Pereira On a nonlinear degenerate evolution equation with strong damping International Journal of Mathematics and Mathematical Sciences weak solutions evolution equation with damping. |
| title | On a nonlinear degenerate evolution equation with strong damping |
| title_full | On a nonlinear degenerate evolution equation with strong damping |
| title_fullStr | On a nonlinear degenerate evolution equation with strong damping |
| title_full_unstemmed | On a nonlinear degenerate evolution equation with strong damping |
| title_short | On a nonlinear degenerate evolution equation with strong damping |
| title_sort | on a nonlinear degenerate evolution equation with strong damping |
| topic | weak solutions evolution equation with damping. |
| url | http://dx.doi.org/10.1155/S016117129200070X |
| work_keys_str_mv | AT jorgeferreira onanonlineardegenerateevolutionequationwithstrongdamping AT ducivalcarvalhopereira onanonlineardegenerateevolutionequationwithstrongdamping |