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

TL;DR

This paper enhances the understanding of a nonlocal pseudo-parabolic equation with conical degeneration by improving solution regularity and establishing finite time blow-up conditions based on initial data, removing previous energy assumptions.

Contribution

It improves regularity results and establishes new blow-up criteria that depend only on the Nehari functional and conservative integral, removing the need for initial energy assumptions.

Findings

Improved regularity of weak solutions.

Finite time blow-up occurs under new initial conditions.

Blow-up criteria depend solely on Nehari functional and conservative integral.

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.