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pseudo-parabolic equation

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Some sharp results about the global existence and blowup of solutions to a class of pseudo-parabolic equations
Part of
- Parabolic equations and systems
- Partial differential equations
Xiaoli Zhu, Fuyi Li, Yuhua Li
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 6 / December 2017

Published online by Cambridge University Press:

14 August 2017, pp. 1311-1331

Print publication:

December 2017
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In this paper we are interested in a sharp result about the global existence and blowup of solutions to a class of pseudo-parabolic equations. First, we represent a unique local weak solution in a new integral form that does not depend on any semigroup. Second, with the help of the Nehari manifold related to the stationary equation, we separate the whole space into two components S+ and S– via a new method, then a sufficient and necessary condition under which the weak solution blows up is established, that is, a weak solution blows up at a finite time if and only if the initial data belongs to S–. Furthermore, we study the decay behaviour of both the solution and the energy functional, and the decay ratios are given specifically.