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Title: Second order quasilinear functional evolution equations (English)
Author: Simon, László
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 140
Issue: 2
Year: 2015
Pages: 139-152
Summary lang: English
Category: math
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. (English)
Keyword: functional evolution equation
Keyword: second order quasilinear equation
Keyword: monotone operator
MSC: 35A01
MSC: 35A02
MSC: 35B35
MSC: 35R10
MSC: 35R20
idZBL: Zbl 06486930
idMR: MR3368490
DOI: 10.21136/MB.2015.144322
Date available: 2015-06-30T12:13:51Z
Last updated: 2020-07-29
Stable URL:
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