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Applied Math Seminar
Generalized fronts passing an obstacle
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This lecture is concerned with reaction-diffusion equations in general non homogeneous media. Two main themes will be considered. The first part deals with spreading properties for equations of the Fisher type in general domains. The role of geometrical properties of the domains will be analyzed. In the second part I will present extended notions of travelling front in general settings and discuss some of their properties. Generalized fronts passing an obstacle are examples of these notions. A construction will be given for bistable reaction-diffusion equations in the case of star-shaped obstacles. It involves some new Liouville type results for associated elliptic problems. This presentation reports on recent joint works with F. Hamel, N. Nadirashvili and H. Matano. |