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

Mathematics

MuhammadZainul Abidin¹  Jiecheng Chen¹ 

[1] College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;

关键词: global well-posedness;    analyticity;    porous medium equation;    Fourier-Besov-Morrey space with variable exponent;   

DOI  :  10.3390/math9050498

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown