Traveling wave solutions of a nonlinear reaction–advection equation

被引：0
|
作者：
Konstadia Lika
Thomas G. Hallam
机构：
[1]  Department of Ecology,
[2] Evolution and Marine Biology,undefined
[3] University of California,undefined
[4] Santa Barbara,undefined
[5] CA 93106,undefined
[6] USA. e-mail: lika@lifesci.ucsb.edu,undefined
[7]  Department of Ecology and Evolutionary Biology,undefined
[8] 569 Dabney Hall,undefined
[9] University of Tennessee,undefined
[10] Knoxville,undefined
[11] TN 37996-1670,undefined
[12] USA. e-mail: hallam@tiem.utk.edu,undefined
[13]  Current address: Department of Biology,undefined
[14] P.O. Box 2208,undefined
[15] University of Crete,undefined
[16] GR-71409 Iraklion,undefined
[17] Crete,undefined
[18] Greece,undefined
来源：
Journal of Mathematical Biology | 1999年 / 38卷
关键词：
Key words: Nonlinear advective processes; Traveling waves; Stability;
D O I：
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中图分类号：
学科分类号：
摘要：
 We establish the existence of traveling wave solutions for a nonlinear partial differential equation that models a logistically growing population whose movement is governed by an advective process. Conditions are presented for which traveling wave solutions exist and for which they are stable to small semi-finite domain perturbations. The wave is of mathematical interest because its behavior is determined by a singular differential equation and those with small speed of propagation steepen into a shock-like solutions. Finally, we indicate that the smoothing presence of diffusion allows wave persistence when an advective slow moving wave may collapse.
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页码：346 / 358
页数：12
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