Blow-up results for damped wave equation with fractional Laplacian and non linear memory
DOI:
https://doi.org/10.24193/subbmath.2022.4.04Keywords:
Damped wave equation, blow-up, Fujita’s exponent, fractional derivative.Abstract
This paper is devoted to find the critical exponent in Fujita’s sense and to prove the blow-up results of solutions for the damped equation with fractional Laplacian and nonlinear memory.
Mathematics Subject Classification (2010): 26A33, 35K55, 74G25, 74H35.
Received 02 February 2020; Accepted 10 May 2020.
References
Biler, P., Karch, G., Woyczynski, W.A., Asymptotics for conservation laws involving Leivy diffusion generators, Studia Mathematica, 148(2001), no. 2, 171-192.
Cazenave, T., Dickstein, F., Weissler, F.D., An equation whose Fujita critical exponent is not given by scaling, Nonlinear Anal., 68(2008), 862-874.
Duistermaat, J.J., H¨ormander, L., Fourier integral II, Acta Math., 128(1972), 183-269. [4] Fino, A., Critical exponent for damped wave equations with nonlinear memory, Hal Arch. Ouv. Id: 00473941v2, (2010).
Hadj Kaddour, T., Hakem, A., Local existence and sufficient conditions of non-global solutions for weighted damped wave equations, Facta Univ. Ser. Math. Inform., 32(2017), no. 5, 629-657.
Hadj Kaddour, T., Hakem, A., Sufficient conditions of non-global solutions for fractional damped wave equations with non-linear memory, Adv. Theory of Nonlinear Analysis Appl., 2(2018), no. 4, 224-237.
Ju, N., The maximum principle and the global attractor for the dissipative 2-D quasi- geostrophic equations, Comm. Pure Appl. Math., (2005), 161-181.
Kilbas, A.A., Sarivastana, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier 2006.
Martinez, A., An Introduction to Semiclassical and Microlocal Analysis Lecture Notes, Universit`a di Bologna, Italy, 2001.
Mitidieri, E., Pohozaev, S.I., Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on Rn, J. Evol. Equ., 1(2001), 189-220.
Mitidieri, E., Pohozaev, S.I., A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities, Proc. Steklov. Inst. Math., 234(2001), 1-383.
Pohozaev, S.I., Tesei, A., Blow-up of nonnegative solutions to quasilinear parabolic inequalities, Atti Accad. Naz. Lincei Cl. Sci. Fis. Math. Natur. Rend. Lincei. 9 Math. App, 11(2000), no. 2, 99-109.
Pozrikidis, C., The fractional Laplacian, Taylor Francis Group, LLC /CRC Press, Boca Raton (USA), 2016.
Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives, Theory and Application, Gordon and Breach Publishers, 1987.
Souplet, P., Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory, Z. Angew. Math. Phys, 55(2004).
Todorova, G., Yardanov, B., Critical exponent for a non linear wave equation with damping, J. Differential Equations, 174(2001), 464-489.
Zhang, Q.S., A Blow Up Result for a Nonlinear Wave Equation with Damping, C.R. Acad. Sci., Paris, 2001.
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