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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296001044 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |