Existence and nonexistence of curved front solution of a biological equation |
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Authors: | Guillemette Chapuisat |
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Affiliation: | Laboratoire de mathématiques, Université Paris-Sud XI, 91405 Orsay cedex, France |
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Abstract: | This paper deals with the existence of curved front solution of a partial differential equation coming from a mathematical model of stroke. The equation is of reaction-diffusion type in a cylinder of radius R and of diffusion and absorption type outside of the cylinder. We prove the nonexistence of a travelling front when R is small enough and the existence if R is large enough using a recent energy method. We construct the travelling front as the limit in time of a solution with a well-chosen initial condition, in a travelling referential. |
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Keywords: | Reaction-diffusion Curved travelling front Phase portrait Energy methods Travelling referential Biology |
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