Existence of weak solutions for abstract hyperbolic-parabolic equations
In this paper we study the Existence and Uniqueness of solutions for the following Cauchy problem:A2u″(t)+A1u′(t)+A(t)u(t)+M(u(t))=f(t), t∈(0,T) (1)u(0)=u0; A2u′(0)=A212u1; where A1 and A2 are bounded linear operators in a Hilbert space H, {A(t)}0≤t≤T is a family of se...
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294001067 |
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| _version_ | 1832558135684890624 |
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| author | Marcondes Rodrigues Clark |
| author_facet | Marcondes Rodrigues Clark |
| author_sort | Marcondes Rodrigues Clark |
| collection | DOAJ |
| description | In this paper we study the Existence and Uniqueness of solutions for the following Cauchy problem:A2u″(t)+A1u′(t)+A(t)u(t)+M(u(t))=f(t), t∈(0,T) (1)u(0)=u0; A2u′(0)=A212u1; where A1 and A2 are bounded linear operators in a Hilbert space H, {A(t)}0≤t≤T is a family of self-adjoint operators, M is a non-linear map on H and f is a function from (0,T) with values in H. |
| format | Article |
| id | doaj-art-d5ea96dcc6cf4b2698e7d4a7da2539ba |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d5ea96dcc6cf4b2698e7d4a7da2539ba2025-02-03T01:33:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117475976910.1155/S0161171294001067Existence of weak solutions for abstract hyperbolic-parabolic equationsMarcondes Rodrigues Clark0Universidade Federal da Paraíba - Campus II - DME - CCT, Campina Grande 58.109-970, Paraíba, BrazilIn this paper we study the Existence and Uniqueness of solutions for the following Cauchy problem:A2u″(t)+A1u′(t)+A(t)u(t)+M(u(t))=f(t), t∈(0,T) (1)u(0)=u0; A2u′(0)=A212u1; where A1 and A2 are bounded linear operators in a Hilbert space H, {A(t)}0≤t≤T is a family of self-adjoint operators, M is a non-linear map on H and f is a function from (0,T) with values in H.http://dx.doi.org/10.1155/S0161171294001067existence of weak solutionsnonlinear equationCauchy problemexistence and uniqueness. |
| spellingShingle | Marcondes Rodrigues Clark Existence of weak solutions for abstract hyperbolic-parabolic equations International Journal of Mathematics and Mathematical Sciences existence of weak solutions nonlinear equation Cauchy problem existence and uniqueness. |
| title | Existence of weak solutions for abstract hyperbolic-parabolic equations |
| title_full | Existence of weak solutions for abstract hyperbolic-parabolic equations |
| title_fullStr | Existence of weak solutions for abstract hyperbolic-parabolic equations |
| title_full_unstemmed | Existence of weak solutions for abstract hyperbolic-parabolic equations |
| title_short | Existence of weak solutions for abstract hyperbolic-parabolic equations |
| title_sort | existence of weak solutions for abstract hyperbolic parabolic equations |
| topic | existence of weak solutions nonlinear equation Cauchy problem existence and uniqueness. |
| url | http://dx.doi.org/10.1155/S0161171294001067 |
| work_keys_str_mv | AT marcondesrodriguesclark existenceofweaksolutionsforabstracthyperbolicparabolicequations |