# Classification of initial energy in a pseudo-parabolic equation with variable exponents

Classification of initial energy in a pseudo-parabolic equation with variable exponents This paper deals with a pseudo-parabolic equation with variable exponents, subject to homogeneous boundary conditions with initial data in H01(Ω)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H_0^1(\varOmega )$$\end{document}. By using energy functional and Nehari functional, we classify blow-up and global existence of weak solutions in variable Sobolev spaces completely for subcritical, critical, and super critical initial energy, respectively. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Classification of initial energy in a pseudo-parabolic equation with variable exponents

, Volume 11 (4) – Aug 7, 2021
19 pages

/lp/springer-journals/classification-of-initial-energy-in-a-pseudo-parabolic-equation-with-zVML9t8lXc
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-021-00583-4
Publisher site
See Article on Publisher Site

### Abstract

This paper deals with a pseudo-parabolic equation with variable exponents, subject to homogeneous boundary conditions with initial data in H01(Ω)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H_0^1(\varOmega )$$\end{document}. By using energy functional and Nehari functional, we classify blow-up and global existence of weak solutions in variable Sobolev spaces completely for subcritical, critical, and super critical initial energy, respectively.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Aug 7, 2021

Keywords: Pseudo-parabolic equation; Variable exponent; Blow-up; Initial energy; Nehari manifold; 35K70; 35A01; 35B44