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

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  • Huafei Di
  • Zefang Song

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.

Suggested Citation

  • Huafei Di & Zefang Song, 2021. "Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-10, March.
    • Handle: RePEc:hin:jnlamp:6668355
    DOI: 10.1155/2021/6668355
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