Qualitative properties of solutions to a nonlinear time-space fractional diffusion equation
Borikhanov M.B. Ruzhansky M. Torebek B.T.
February 2023Springer Nature
Fractional Calculus and Applied Analysis
2023#26Issue 1111 - 146 pp.
In the present paper, we study the Cauchy-Dirichlet problem to a nonlocal nonlinear diffusion equation with polynomial nonlinearities D0|tαu+(-Δ)psu=γ|u|m-1u+μ|u|q-2u,γ,μ∈R,m>0,q>1, involving time-fractional Caputo derivative D0|tα and space-fractional p-Laplacian operator (-Δ)ps. We give a simple proof of the comparison principle for the considered problem using purely algebraic relations, for different sets of γ, μ, m and q. The Galerkin approximation method is used to prove the existence of a local weak solution. The blow-up phenomena, existence of global weak solutions and asymptotic behavior of global solutions are classified using the comparison principle.
Blow-up and global solution , Comparison principle , Fractional calculus , Quasilinear parabolic equation
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Khoja Akhmet Yassawi International Kazakh–Turkish University, Sattarkhanov ave., 29, Turkistan, 161200, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Khoja Akhmet Yassawi International Kazakh–Turkish University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
School of Mathematical Sciences
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