Traveling waves for a boundary reaction-diffusion equation

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• 作者：L. Caffarelli^a ; ¹ ; ^{caffarel@math.utexas.edu} ; A. Mellet^b ; ² ; ^{mellet@math.umd.edu} ; Y. Sire^c ; ^{sire@cmi.univ-mrs.fr}
• 关键词：Boundary reaction&ndash ; diffusion equation ; Traveling waves ; Free boundary problem
• 刊名：Advances in Mathematics
• 出版年：2012
• 期刊代码：62_00018708
• 类别：mt
• 出版时间：1 June, 2012
• 卷：230
• 期：2
• 页码：433-457
• 文件大小：190 K

摘要

We prove the existence of a traveling wave solution for a boundary reaction-diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for traveling wave solutions of a free boundary problem obtained as singular limit for the reaction-diffusion equation (the so-called high energy activation energy limit). This explicit formula, which is interesting in itself, also allows us to get an estimate on the decay at infinity of the traveling wave (which turns out to be faster than the usual exponential decay).