Traps , Patches , Defects , and Spots : An Asymptotic Analysis of Localized Solutions to Some Diffusive and Reaction - Diffusion Systems
نویسنده
چکیده
We will survey some recent results on construction of entire solutions of semilinear elliptic equations. We will mostly focus on the construction of families of solutions to the Allen-Cahn equation of phase transitions, whose level sets suitable scaled concentrate around a given minimal surface. To do so, we shall introduce an infinite-dimensional form of Lyapunov-Schmidt reduction suitable for this and various related questions. Traps, Patches, Defects, and Spots: An Asymptotic Analysis of Localized Solutions to Some Diffusive and Reaction-Diffusion Systems Professor Michael J. Ward Department of Mathematics, University of British Columbia
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تاریخ انتشار 2011