Global Existence for some Neutral Functional Integrodifferential Equations with Finite Delay | Chapter 14 | Recent Advances in Mathematical Research and Computer Science Vol. 1

In this paper, we look at a family of neutral partial functional integrodifferential equations in Banach spaces that have a finite delay. The worldwide existence, uniqueness, and regularity of solutions with values in the subspace D are of interest to us (A). The technique is based on Banach's fixed point theorem and the graph norm technique. The nonlinear term is regarded as a perturbation of the linear equation in our research. We use a diffusive neutral partial functional integrodifferential equation as an example.

Author (S) Details

Sylvain Koumla
Departement de Mathematiques, Faculty des Sciences et Techniques, University Adam Barka, B.P. 1117, Abeche, Tchad.

Djaokamla Temga
Departement de Mathematiques, Faculty des Sciences et Techniques, University Adam Barka, B.P. 1117, Abeche, Tchad.

Abdou Sene
Departement de Mathematiques, University Virtuelle de Dakar, Senegal.

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Study on Partial Functional Integrodifferential Equations | Chapter 12 | Recent Advances in Mathematical Research and Computer Science Vol. 1

Many authors have focused their attention in recent years on the study of existence problems for differential and integrodifferntial equations. The existence and regularity of solutions for several partial functional integrodifferential equations with finite delay are investigated in this paper. The asymptotic stability and continuous dependency of initial values are also investigated. To begin, we demonstrate the existence of mild solutions. Second, we provide sufficient conditions to ensure that stringent solutions exist. The method uses concepts from linear semigroup theory to treat equations in the domain of A with the graph norm. We end this effort with an application to demonstrate our abstract solution.

 

Author (S) Details

Khalil Ezzinbi
Departement de Mathematiques, Faculte des Sciences Semlalia, Universit Cadi Ayyad, Marrakech, Morocco.

Sylvain Koumla
Departement de Mathematiques, Faculte des Sciences et Technique, Universit Adam Barka, Abeche, Chad.

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