Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations

Huafei Di and Zefang Song

Advances in Mathematical Physics, 2021, vol. 2021, 1-10

Abstract:

This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations . At low initial energy level ( ), we not only prove the existence of global weak solutions for these problems by the combination of the Galerkin approximation and potential well methods but also obtain the finite time blow-up result by adopting the potential well and improved concavity skills. Finally, we also discussed the finite time blow-up phenomenon for certain solutions of these problems with high initial energy.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:6668355

DOI: 10.1155/2021/6668355

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