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On weak solutions of semilinear hyperbolic-parabolic equations. (English) Zbl 0861.35062
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.

MSC:
35L80 Degenerate hyperbolic equations
35M10 PDEs of mixed type
35D05 Existence of generalized solutions of PDE (MSC2000)
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