Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent

Muhammad Zainul Abidin and Jiecheng Chen
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Muhammad Zainul Abidin: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Jiecheng Chen: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2021, vol. 9, issue 5, 1-13

Abstract: In this paper, we consider the generalized porous medium equation. For small initial data u 0 belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using the Fourier localization principle and the Littlewood-Paley decomposition technique. Furthermore, we also show Gevrey class regularity of the solution.

Keywords: global well-posedness; analyticity; porous medium equation; Fourier-Besov-Morrey space with variable exponent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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