Higher Regularity and Finite Time Blow-up to Nonlocal Pseudo-parabolic Equation with Conical Degeneration

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(...

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Bibliographic Details
Published in:Applied mathematics & optimization 2023-10, Vol.88 (2), p.50, Article 50
Main Authors: Meng, Jingbo, Xu, Guangyu
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary value problems
Calculus of Variations and Optimal Control
Optimization
Control
Degeneration
Energy
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Parabolic differential equations
Regularity
Simulation
Systems Theory
Theoretical
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Summary: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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-023-10031-3