Higher order models for waves in nonlinear, dispersive media
Jerry Bona | University of Illinois at Chicago - Estados Unidos
Well-posedness of the Cauchy problem and stability theory for nonlinear dispersive...
| Grant number: | 20/14833-8 |
| Support Opportunities: | Regular Research Grants |
| Duration: | April 01, 2021 - March 31, 2023 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Mahendra Prasad Panthee |
| Grantee: | Mahendra Prasad Panthee |
| Host Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
| Associated researchers: | Xavier Carvajal Paredes |
Abstract
In this project we consider nonlinear evolution equations of dispersive type. Our principal objective is the study of the Acauchy problems associated to dispersive models. More precisely, we study the local and global existence, controllability, stabilization, stability of solitary wave solutions, analyticity of solutions and unique continuation property (UCP) of solutions and their generalization. The main models considered in this project are the nonlinear Schrödinger equation (NLS), Korteweg-de Vries equation (KdV), Benjamin-Ono equations, Intermediate long wave (ILW) equation and systems involving these equations. We will consider these models posed in euclidean domains as well as in Riemannian manifolds. (AU)
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