BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS
Abstract
Keywords
References
- Ball J. M., "Remarks on blow-up and nonexistence theorems for nonlinear evolution equations", Quart. J. Math. Oxford Ser., 28, 473-486, 1977.
- Cavalcanti M.M., Domingos Cavalcanti V.N., Ferreira J., "Existence and uniform decay for nonlinear viscoelastic equation with strong damping", Math. Methods Appl. Sci., 24, 1043-1053, 2001.
- Chen Y., Levine S., Rao M., "Variable Exponent, Linear Growth Functionals in Image Restoration", SIAM Journal on Applied Mathematics, 66, 1383-1406, 2006.
- Diening L., Hasto P., Harjulehto P., Ruzicka M.M., "Lebesgue and Sobolev Spaces with Variable Exponents", Springer-Verlag, 2011. Fan X.L., Shen J.S., Zhao D., "Sobolev embedding theorems for spaces W^{k,p(x)}(Ω)", J. Math. Anal. Appl., 263, 749-760, 2001.
- Georgiev V., Todorova G., "Existence of a solution of the wave equation with nonlinear damping and source term", J. Differ. Equations, 109, 295-308, 1994.
- Kalantarov V.K., Ladyzhenskaya O.A., "The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types", J. Soviet Math., 10, 53-70, 1978.
- Kovacik O., Rakosnik J., "On spaces L^{p(x)}(Ω), and W^{k,p(x)}(Ω)", Czechoslovak Mathematical Journal, 41, 592-618, 1991.
- Levine H.A., "Instability and nonexistence of global solutions of nonlinear wave equations of the form Pu_{tt}=Au+F(u)", Trans. Amer. Math. Soc., 192, 1-21, 1974.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Erhan Pişkin
*
0000-0001-6587-4479
Türkiye
Publication Date
December 30, 2019
Submission Date
September 10, 2019
Acceptance Date
December 6, 2019
Published in Issue
Year 2019 Volume: 5 Number: 2
Cited By
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