Global existence and energy decay for a transmission problem under a boundary fractional derivative type-Reference-Cited by-同舟云学术

Global existence and energy decay for a transmission problem under a boundary fractional derivative type

Published:2023 Issue:11 Volume:8 Page:27605-27625
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Bahri Noureddine¹²,Beniani Abderrahmane³,Braik Abdelkader¹⁴,Georgiev Svetlin G.⁵,Hajjej Zayd⁶,Zennir Khaled⁷

Affiliation:

1. Faculty of Science and Technology, Hasiba Benbouali University, Chlef 02000-Algeria

2. Laboratory of Mathematics and Applications, Hassib Benbouali University, Chlef 02000, Algeria

3. Department of Mathematics, University Ain Tmouchent, Belhadj Bouchaib, B.P. 284 RP, Ain Temouchent 46000, Algeria

4. Laboratory of Fundamental and Applicable Mathematics of Oran, University of Oran1 Ahmed Ben Bella, B.P. 1524 El M'naouar, Oran 31000, Algeria

5. Department of Mathematics, Sorbonne University, 75005, Paris, France

6. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

7. Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma. B.P. 401 Guelma 24000 Algérie

Abstract

<abstract><p>The paper considers the effects of fractional derivative with a high degree of accuracy in the boundary conditions for the transmission problem. It is shown that the existence and uniqueness of the solutions for the transmission problem in a bounded domain with a boundary condition given by a fractional term in the second equation are guaranteed by using the semigroup theory. Under an appropriate assumptions on the transmission conditions and boundary conditions, we also discuss the exponential and strong stability of solution by also introducing the theory of semigroups.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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