On weak solutions of semilinear hyperbolic-parabolic equations
In this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equation (K1(x,t)u′)′+K2(x,t)u′+A(t)u+F(u)=f with null Dirichlet boundary conditions and zero initial data, where F(s) is a continuous function such that sF(s)≥0, ∀s∈R a...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1996-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296001044 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849403166137778176 |
|---|---|
| author | Jorge Ferreira |
| author_facet | Jorge Ferreira |
| author_sort | Jorge Ferreira |
| collection | DOAJ |
| description | In this paper we prove the existence and uniqueness of weak solutions of the mixed
problem for the nonlinear hyperbolic-parabolic equation
(K1(x,t)u′)′+K2(x,t)u′+A(t)u+F(u)=f
with null Dirichlet boundary conditions and
zero initial data, where F(s) is a continuous function such
that sF(s)≥0, ∀s∈R and {A(t);t≥0} is a family of operators of L(H01(Ω);H−1(Ω)).
For the
existence we apply the Faedo-Galerkin method with
an unusual a priori estimate and a result of
W. A. Strauss. Uniqueness is proved only for some
particular classes of functions F. |
| format | Article |
| id | doaj-art-933322ec92a8473f8ca43417ca8b5f76 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-933322ec92a8473f8ca43417ca8b5f762025-08-20T03:37:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119475175810.1155/S0161171296001044On weak solutions of semilinear hyperbolic-parabolic equationsJorge Ferreira0Departamento de Matemática, Universidade Estadual de Maringá, Agência Postal UEM, Maringá 87020-900, PR, BrazilIn this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equation (K1(x,t)u′)′+K2(x,t)u′+A(t)u+F(u)=f with null Dirichlet boundary conditions and zero initial data, where F(s) is a continuous function such that sF(s)≥0, ∀s∈R and {A(t);t≥0} is a family of operators of L(H01(Ω);H−1(Ω)). For the existence we apply the Faedo-Galerkin method with an unusual a priori estimate and a result of W. A. Strauss. Uniqueness is proved only for some particular classes of functions F.http://dx.doi.org/10.1155/S0161171296001044Weak solutionssemilinear hyperbolic-parabolic equation degenerating equations. |
| spellingShingle | Jorge Ferreira On weak solutions of semilinear hyperbolic-parabolic equations International Journal of Mathematics and Mathematical Sciences Weak solutions semilinear hyperbolic-parabolic equation degenerating equations. |
| title | On weak solutions of semilinear hyperbolic-parabolic equations |
| title_full | On weak solutions of semilinear hyperbolic-parabolic equations |
| title_fullStr | On weak solutions of semilinear hyperbolic-parabolic equations |
| title_full_unstemmed | On weak solutions of semilinear hyperbolic-parabolic equations |
| title_short | On weak solutions of semilinear hyperbolic-parabolic equations |
| title_sort | on weak solutions of semilinear hyperbolic parabolic equations |
| topic | Weak solutions semilinear hyperbolic-parabolic equation degenerating equations. |
| url | http://dx.doi.org/10.1155/S0161171296001044 |
| work_keys_str_mv | AT jorgeferreira onweaksolutionsofsemilinearhyperbolicparabolicequations |