On the global existence and analyticity of the mild solution for the fractional Porous medium equation

In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main objectives of studying the fractional porous medium equation in the corresponding critical function spaces are to show the existence of unique global mil...

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Bibliographic Details
Published in:Boundary value problems 2023-11, Vol.2023 (1), p.107-8, Article 107
Main Authors: Abidin, Muhammad Zainul, Marwan, Muhammad
Format: Article
Language:English
Subjects:
Analysis
Analyticity
Approximations and Expansions
Boundary value problems
Critical spaces
Difference and Functional Equations
Fourier transforms
Fractional porous medium equation
Function space
Global solution
Groundwater
Integral equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Porous materials
Porous media
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Summary:In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main objectives of studying the fractional porous medium equation in the corresponding critical function spaces are to show the existence of unique global mild solution under the condition of small initial data. Applying Fourier transform methods gives an equivalent integral equation of the model equation. The linear and nonlinear terms are then estimated in the corresponding Lei and Lin spaces. Further, the analyticity of solution to the fractional Porous medium equation is also obtained.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-023-01794-3