Research Article

BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS

Volume: 5 Number: 2 December 30, 2019
EN

BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS

Abstract

The aim of this work is to study the blow up of solutions for the viscoelastic wave equation with variable exponents in a bounded domain. Our result extends the one in <cite>Messaoudi1</cite> to problems with variable exponent nonlinearities.

Keywords

References

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  2. 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.
  3. Chen Y., Levine S., Rao M., "Variable Exponent, Linear Growth Functionals in Image Restoration", SIAM Journal on Applied Mathematics, 66, 1383-1406, 2006.
  4. 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.
  5. 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.
  6. 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.
  7. Kovacik O., Rakosnik J., "On spaces L^{p(x)}(Ω), and W^{k,p(x)}(Ω)", Czechoslovak Mathematical Journal, 41, 592-618, 1991.
  8. 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

Publication Date

December 30, 2019

Submission Date

September 10, 2019

Acceptance Date

December 6, 2019

Published in Issue

Year 2019 Volume: 5 Number: 2

APA
Pişkin, E. (2019). BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS. Middle East Journal of Science, 5(2), 134-145. https://doi.org/10.23884/mejs.2019.5.2.05
AMA
1.Pişkin E. BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS. MEJS. 2019;5(2):134-145. doi:10.23884/mejs.2019.5.2.05
Chicago
Pişkin, Erhan. 2019. “BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS”. Middle East Journal of Science 5 (2): 134-45. https://doi.org/10.23884/mejs.2019.5.2.05.
EndNote
Pişkin E (December 1, 2019) BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS. Middle East Journal of Science 5 2 134–145.
IEEE
[1]E. Pişkin, “BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS”, MEJS, vol. 5, no. 2, pp. 134–145, Dec. 2019, doi: 10.23884/mejs.2019.5.2.05.
ISNAD
Pişkin, Erhan. “BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS”. Middle East Journal of Science 5/2 (December 1, 2019): 134-145. https://doi.org/10.23884/mejs.2019.5.2.05.
JAMA
1.Pişkin E. BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS. MEJS. 2019;5:134–145.
MLA
Pişkin, Erhan. “BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS”. Middle East Journal of Science, vol. 5, no. 2, Dec. 2019, pp. 134-45, doi:10.23884/mejs.2019.5.2.05.
Vancouver
1.Erhan Pişkin. BLOW UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH VARIABLE EXPONENTS. MEJS. 2019 Dec. 1;5(2):134-45. doi:10.23884/mejs.2019.5.2.05

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