The critical exponent for nonlinear wave equation with structural damping

• Grant number: 22/16487-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: July 17, 2023
• End date: July 21, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Rempel Ebert
• Grantee: Marcelo Rempel Ebert
• Visiting researcher: Marcello Dabbicco
• Visiting researcher institution: Università degli Studi di Bari - Aldo Moro, Italy
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this project, we are interested in the asymptotic behavior (in time) of solutions to the Cauchy problem for a strongly damped wave equation in Lebesgue or Sobolev spaces. We plan to apply these estimates to study semi-linear problems. In particular, we are interested in proving results about global existence (in time) of the solutions, possibly assuming small initial data. Also blow-up results and the life-span of solutions are topics of interest. (AU)