Bounded weak solutions to a class of parabolic equations with gradient term and Lr(0,T;Lq(?)) sources
Received:April 16, 2021  Revised:August 10, 2021
Key Word: Parabolic equations   Lower order gradient term   L∞ estimate   Bounded solutions.  
Fund ProjectL:National Science Foundation of China (11901131)
Author NameAffiliationAddress
Zhongqing Li School of mathematics and statisticsGuizhou university of finance and economics School of mathematics and statistics of Guizhou university of finance and economics in Guiyang city of Guizhou province
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      We prove an existence result to a class of nonlinear parabolic equations. The purpose of this paper is to prove, under suitable assumptions on the integrability of the space Lr(0,T;Lq(?)) for the source terms and the coefficient of the gradient term, an a priori L∞ estimate and the existence of bounded solutions. The methods consist of constructing a family of perturbation problems by regularization, Stampacchia’s iterative technique fulfilled by an appropriate nonlinear test function and compactness argument for the limit process.
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