On a system of nonlinear partial functional differential equations of different types
Keywords:
Semilinear hyperbolic equation, quasilinear parabolic equation, partial functional differential equation.Abstract
We consider a system of a semilinear hyperbolic functional differential equation (where the lower order terms contain functional dependence on the unknown function) and a quasilinear parabolic functional differential equation with initial and boundary conditions. Existence of weak solutions for $t\in (0,T)$ and for $t\in (0,\infty )$ will be shown and some qualitative properties of the solutions in $(0,\infty )$ will be formulated.
Mathematics Subject Classification (2010): 35M33.
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