The existence of heteroclinic orbits, and applications
The existence of heteroclinic orbits, and applications
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DOI：
10.1007/3-540-07171-7_14
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
C. Conley;J. Smoller
中科院分区：
文献类型：
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作者：
C. Conley;J. Smoller
密歇根大学，安娜堡，密歇根48104 i.引言物理和生物科学中出现的许多问题都与构造非线性偏微分方程组的行波解有关。也就是说，给定一个形式为(I)u+f(U)x=..~B(U)Ux]xt-~<；x<；~，t>；0的偏微分方程组，我们寻求形式(I)的解(2)u=u(~)，~=x-ct，其中c是一个常数，或者是预先给定的，或者是作为问题的一部分来确定的。这里f是光滑向量值函数，B(U)是正定(或半定)矩阵值函数。如果我们把(2)代成(I)，我们就得到一个下列类型的常微分方程组：D
University of Michigan, Ann Arbor, Michigan 48104 i. Introduction Many questions arising in the physical and biological sciences• are concerned with constructing traveling wave solutions of a system of nonlinear partial differential equations. That is, given a system of partial differential equations of the form (i) u+ f (u) x=..~ B (U) Ux] x t-~< x<~, t> 0, we seek a solution of (i) of the form (2) u= u (~),~= x-ct, where c is a constant, either given beforehand, or to be determined as part of the problem. Here f is a smooth vector-valued function and B (u) is a positive definite (or semidefinite) matrix-valued function. If we substitute (2) into (i), we are led to a system of ordinary differential equations of the following type: d