Global Existence and Blow-up for a Class of Parabolic Equations with Nonhomogeneous Memory Terms
The purpose of this paper is to study the Cauchy problem for a class of parabolic equations with non-homogeneous memo-ry term.This paper investigates the influence of nonlinear and non-homogeneous terms on the existence of global solutions.When the exponential growth of the nonlinear term is higher than a certain number,the existence and uniqueness of the global solution are proved by using the contraction mapping principle.Using the test function method,this paper proves that the solution blows up in fi-nite time when the exponential growth of the nonlinear term is lower than a certain number.
Cauchy problemcontraction mapping principletest function methodglobal existenceBlow-up
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