# zbMATH — the first resource for mathematics

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)
##### Keywords:
uniqueness; existence of weak solutions
Full Text: