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Second order quasilinear functional evolution equations. (English) Zbl 1349.35392
Summary: We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in $$(0,T)$$ is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in $$(0,\infty)$$ (boundedness and stabilization as $$t\to \infty$$) are shown.
##### MSC:
 35R10 Partial functional-differential equations
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