Study on the solution of a class of semilinear parabolic equations with singular term
The initial boundary value problem for a class of semilinear parabolic equations with singular term and logarithmic source is considered.The difficulty of dealing with singular term by regularization method,the local existence of the weak solution is obtained by approximating the truncation function.By means of logarithmic Sobolev inequality and potential well method,the global existence of the weak solution is proved in critical and subcritical cases.The decay estimation of the global solution is given by using the potential well family and differential inequality.
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