Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation

Ercan ÇELİK

In this study, the Lie symmetry analysis is given for the time-fractional telegraph equation with the Riemann-Liouville derivative. This equation is useable to describe the physical processes of models possessing memory. By applying classical and nonclassical Lie symmetry analysis for the telegraph equation with & alpha;,& beta; time-fractional derivatives and some technical computations, new infinitesimal generators are obtained. The actual methods give some classical symmetries while the nonclassical approach will bring back other symmetries to these equations. The similarity reduction and c ...Более

Статья 2023 Fen Fakültesi Advances in Mathematical Physics2023 14 Просмотры

Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

Ercan ÇELİK

In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo-Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents p & sdot; and q & sdot;. Finally, we prove a finite-time blow-up result for negative initial energy. Keyword: global existence; wave-equation

Статья 2023 Fen Fakültesi Advances in Mathematical Physics2023 18 Просмотры

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Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation

Ercan ÇELİK

Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

Ercan ÇELİK