Existence Result to a Class of Parabolic Equations with Nonstandard Growth Condition and Zero Order Term
Received:September 18, 2022  Revised:January 08, 2023
Key Words: nonstandard growth condition   zero order term   weak solutions  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11901131) and the University-Level Research Fund Project in Guizhou University of Finance and Economics (Grant No.2022KYYB01).
Author NameAffiliation
Zhongqing LI School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
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      In the setting of variable exponent, an existence result to a class of parabolic equations with zero order term is proved. The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously. By virtue of a priori estimates and some limit analyses, the weak limit of the nonlinear principal term is identified via the Young measures method.
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