Semilinear Caputo time-fractional pseudo-parabolic equations

Abstract

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.