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El-Gamel, M., El-Baghdady, G.I. and El-Hady, M.A. (2022) Highly Efficient Method for Solving Parabolic PDE with Nonlocal Boundary Conditions. Applied Mathematics, 13, 101-119.
https://doi.org/10.4236/am.2022.132009

has been cited by the following article:

• TITLE: Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

  AUTHORS: Xiaoxin Yang

  KEYWORDS: Nonlocal Parabolic Equation, Singular Potential, Logarithmic Nonlocal Source, Global Existence, Decay

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.1, January 29, 2024

  ABSTRACT: This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.