Electron. J. Diff. Equ., Vol. 2016 (2016), No. 172, pp. 1-11.

Cauchy problem for some fractional nonlinear ultra-parabolic equations

Fatma Al-Musalhi, Sebti Kerbal

Abstract:
Blowing-up solutions to nonlocal nonlinear ultra-parabolic equations is presented. The obtained results will contribute in the development of ultra-parabolic equations and enrich the existing non-extensive literature on fractional nonlinear ultra-parabolic problems. Our method of proof relies on a suitable choice of a test function and the weak formulation approach of the sought for solutions.

Submitted April 10, 2016. Published July 5, 2016.
Math Subject Classifications: 35A01, 26A33, 35K70.
Key Words: Nonexistence; nonlinear ultra-parabolic equations; nonlocal space and time operators.

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Fatma Al-Musalhi
Department of Mathematics and Statistics
Sultan Qaboos University,P.O. Box 36
Al-Khodh 123, Muscat, Oman
email: p070293@student.squ.edu.om
Sebti Kerbal
Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36
Al-Khodh 123, Muscat, Oman
email: skerbal@squ.edu.om

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