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Semilinear Caputo time-fractional pseudo-parabolic equations. (English) Zbl 1460.35381

Summary: This paper considers two problems: the initial boundary value problem of nonlinear Caputo time-fractional pseudo-parabolic equations with fractional Laplacian, and the Cauchy problem (initial value problem) of Caputo time-fractional pseudo-parabolic equations. For the first problem with the source term satisfying the globally Lipschitz condition, we establish the local well-posedness theory including existence, uniqueness and regularity of the local solution, and the further local existence theory related to the finite time blow-up are also obtained for the problem with logarithmic nonlinearity. For the second problem with the source term satisfying the globally Lipschitz condition, we prove the global existence theorem.

MSC:

35R11 Fractional partial differential equations
35B44 Blow-up in context of PDEs
26A33 Fractional derivatives and integrals
33E12 Mittag-Leffler functions and generalizations
35B40 Asymptotic behavior of solutions to PDEs
35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35K20 Initial-boundary value problems for second-order parabolic equations
44A20 Integral transforms of special functions
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