The Role of Dissipation in the Existence of Time-Periodic Solutions to PDE Systems
Centre International de Rencontres Mathématiques via YouTube
Overview
Watch a 29-minute mathematics conference talk exploring how dissipation affects time-periodic solutions in partial differential equation systems. Delve into the phenomenon of resonance in mechanical systems with energy conservation, examining examples like wave equations and linearized elasticity. Learn how strong dissipation in systems like the heat equation prevents resonance by ensuring unique time-periodic solutions. Analyze the heat-wave system as a simplified fluid-structure interaction model to understand the minimum dissipation needed to prevent resonance. Discover how geometric configurations influence solution uniqueness, explore regularity requirements for forcing terms, and consider open questions about resonance occurrence in arbitrary geometries. Recorded at the "Mathematics of fluids in motion: Recent results and trends" meeting at Centre International de Rencontres Mathématiques in Marseille, France, this presentation includes chapter markers, keywords, abstracts, and bibliographies for enhanced learning.
Syllabus
Boris Muha: The Role of Dissipation in the Existence of Time-Periodic Solutions to PDE Systems
Taught by
Centre International de Rencontres Mathématiques