Initial boundary value problems for evolution equations

• Grant number: 24/18973-0
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2025
• End date: March 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Priscila Leal da Silva
• Grantee: Priscila Leal da Silva
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Dionyssios Mantzavinos

Abstract

In this project we propose the study of initial boundary value problems (IBVP) for evolution equations by making use of Fokas' method (UTM). Such method arises as an extension of the inverse scattering transform (IST) to solve initial value problems for the so-called integrable equations, that is, equations that admit solitons as solutions. The UTM is a sort of extension of the Fourier transform to the half-line, in a way that its application provides an expression called global relation that can be deformed in the complex plane in a way to exhibit a solution for the equation under consideration.In particular, the main objectives of this project tackle the investigation of existence and uniqueness of solutions for IBVPs associated to NLS-type dispersive equations, Camassa-Holm type equations and extension of more standardised methods such as Kato's method and the parabolic regularisation. (AU)