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

Huafei Di | Zendy; Zefang Song | Zendy

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

Author(s) -

Huafei Di,

Zefang Song

Publication year - 2021

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2021/6668355

Subject(s) - class (philosophy) , nonlinear system , mathematics , boundary value problem , value (mathematics) , mathematical analysis , computer science , physics , statistics , artificial intelligence , quantum mechanics

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.

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