Existence and multiplicity of global classical solutions for approximate long water wave (ALWW) equations

Azib, Riyadh; Georgiev, Svetlin; Kheloufi, Arezki; Mebarki, Karima

doi:10.22075/ijnaa.2022.27436.3599

Existence and multiplicity of global classical solutions for approximate long water wave (ALWW) equations

Document Type : Research Paper

Authors

Riyadh Azib ¹

Svetlin Georgiev ²

Arezki Kheloufi ¹

Karima Mebarki ¹

¹ Department of Mathematics, Faculty of Exact Sciences, Laboratory of Applied Mathematics, Bejaia University, 06000 Bejaia, Algeria

² Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria

10.22075/ijnaa.2022.27436.3599

Abstract

In this paper, we investigate the Cauchy problem for long water wave equations for the existence and nonuniqueness of global classical solutions. We give sufficient conditions on the initial data of the considered equations that guarantee the existence and multiplicity of nonnegative global classical solutions. For this goal, a new topological approach to the fixed point theory of the sum of two operators in Banach spaces is used.

Keywords

Approximate long water wave equations

classical solution

fixed point

initial value problem