Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations. (10th March 2021)

• Record Type: Journal Article
• Authors: Di, Huafei; Song, Zefang
• Other Names: Rabiei F. Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2021(2021)
• Publication Date: 2021-03-10
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2021/6668355
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations u t − β u x x − k u x x t + γ u x x x x = f u x x . At low initial energy level (J u 0 < d ), 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.