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

Document Type : Research Paper


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


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.


Volume 14, Issue 1
January 2023
Pages 437-450
  • Receive Date: 09 June 2022
  • Accept Date: 05 September 2022