László Simon, Institute of Mathematics, Loránd Eötvös University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary, e-mail: simonl@cs.elte.hu
Abstract: 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.
Keywords: functional evolution equation; second order quasilinear equation; monotone operator
Classification (MSC 2010): 35R10
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