Second order quasilinear functional evolution equations

Simon, László

Mathematica Bohemica, Tome 140 (2015) no. 2, pp. 139-152

Abstract (VO)

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.

Détail

DOI : 10.21136/MB.2015.144322

Classification : 35A01, 35A02, 35B35, 35R10, 35R20
Keywords: functional evolution equation; second order quasilinear equation; monotone operator

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