Nonlinear partial differential equations and propagation phenomena

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This project of strategic basic research aims to develop new mathematics in nonlinear partial differential equations to better understand the propagation phenomena arising in a variety of applications, such as the spreading of infectious diseases or cancerous cells, or the invasion of alien species. New models of partial differential equations over spatial regions with moving boundaries will be introduced and systematically studied to provide deep understanding of the mechanisms of important new phenomena in propagation, including accelerated spreading and the onset of such spreading. The mathematical questions are concerned with the long-time dynamics of equations with free boundary, and the asymptotic profiles of their solutions.