On initial value problem for diffusion equation with Caputo-Fabrizio operator on the plane

Vo Ngoc Minh; Le Dinh Long

doi:10.3934/dcdss.2023196

Article Contents

2024, Volume 17, Issue 3: 1293-1309. Doi: 10.3934/dcdss.2023196

This issue Previous Article Limiting behavior of invariant or periodic measure of Hopfield neural models driven by locally Lipschitz Lévy noise Next Article The index theory for multivalued dynamical systems with applications to reaction-diffusion equations with discontinuous nonlinearity

On initial value problem for diffusion equation with Caputo-Fabrizio operator on the plane

Vo Ngoc Minh^{1, 2,} and
Le Dinh Long^3, ,

1.
Faculty of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu St., Vietnam
2.
Vietnam National University, Ho Chi Minh City, Vietnam
3.
Falculty of Maths, FPT University HCM, Saigon Hi-tech Park, Ho Chi Minh City, Vietnam

^*Corresponding author: Le Dinh Long (longld13@fe.edu.vn). Email of other author: vongocminh200520@gmail.com (Vo Ngoc Minh)
^*Corresponding author: Le Dinh Long (longld13@fe.edu.vn). Email of other author: vongocminh200520@gmail.com (Vo Ngoc Minh)

Document Type: Research Article.

Received: June 2023

Revised: October 2023

Early access: October 26, 2023

Published online: October 26, 2023

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Abstract

In this paper, we are interested in studying the diffusion equation with Caputo-Fabrizio derivative. This is the first time that the Caputo-Fabrizio problem on the $ \mathbb R^2 $ domain has been studied. Under the various assumptions of the initial datum and the source functions, we provide the upper bound of the mild solution. We also obtain the upper bound of the first derivative and Caputo-Fabrizio derivative of the mild solution. In addition, we obtain the lower bound of the mild solution and its derivative.

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Mathematics Subject Classification: 35R11, 35B65, 26A33.

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References

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