Research Project: Doğrusal Olmayan Sönümlü Dalga Denklemlerin ve Doğrusal Olmayan Parabolik Denklemlerin Çözümlarinin Patlaması
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Contributors
Funders
ID
TB.00131
Authors
Kalantarov, Varga
Faculty Member
Publications
Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations
(Academic Press Inc Elsevier Science, 2013) Bilgin, Bilgesu Arif; Kalantarov, Varga; Department of Mathematics; Yes; College of Sciences
We obtain sufficient conditions on initial functions for which the initial boundary value problem for second order quasilinear strongly damped wave equations blow up in a finite time.
A note on a strongly damped wave equation with fast growing nonlinearities
(American Institute of Physics (AIP) Publishing, 2015) Kalantarov, Varga; Zelik, Sergey; Department of Mathematics; Yes; College of Sciences
A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the nonlinearities involved, the initial boundary value problem for the considered equation is globally well-posed in the class of sufficiently regular solutions and the semigroup generated by the problem possesses a global attractor in the corresponding phase space. These results are obtained for the nonlinearities of an arbitrary polynomial growth and without the assumption that the considered problem has a global Lyapunov function. (C) 2015 AIP Publishing LLC
