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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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