Higher regularity and finite time blow-up to nonlocal pseudo-parabolic equation with conical degeneration

Abstract

This paper deals with the initial-boundary value problem to a nonlocal semilinear pseudo-parabolic equation with conical degeneration, which has been studied in [Global well-posedness for a nonlocal semilinear pseudo-parabolic equation with conical degeneration, J. Differential Equations, 2020, 269(5): 4566--4597]. We first improve the regularity of the weak solution, and then study finite time blow-up phenomenon for the problem. Our initial condition for blow-up only depends on Nehari functional and the conservative integral, which suggests that the assumption of initial energy functional in the original paper can be removed.

Accepted and in press in Applied Mathematics and Optimization. Comments are welcome