On a Stefan-type model arising in ecology |
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| Institution: | 1. Institute of Mathematics of Academy of Sciences, 252601 Kiev, Tereschenkovskaya 3, Ukraine;2. University of Pécs, PMMK, H-7624, Pécs, Boszorkány u. 2., Hungary;3. Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands |
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| Abstract: | We discuss the dispersal of a chemical, emitted from a point source, into a reacting medium. The diffusion and reaction are such that a front emerges, so that at all times the chemical remains confined to a bounded domain around the source. We focus on the final stationary state which is a non-standard Stefan-type boundary value problem for an Emden–Fowler equation. We prove its existence and uniqueness and obtain, analytically as well as numerically, bounds for the location of the front and for the concentration profile. |
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