On weak solutions of semilinear hyperbolic-parabolic equations (Q1922854)
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scientific article; zbMATH DE number 930053
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On weak solutions of semilinear hyperbolic-parabolic equations |
scientific article; zbMATH DE number 930053 |
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On weak solutions of semilinear hyperbolic-parabolic equations (English)
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4 May 1997
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The author considers a mixed problem for the semilinear hyperbolic-parabolic equation \[ (K_1(x,t)u')'+ K_2(x,t)u'+A(t)u+F(u)= f, \] where \(K_1\geq 0\), \(A(t)\) is an elliptic operator of the second order, and \(F(u)\) is a continuous function. Using the theorem of W. Strauss on a weak convergence, he proves the existence of weak solutions. Examples of \(F(u)\) are given when the solution obtained is unique.
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uniqueness
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existence of weak solutions
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