Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation
Partial differential equations and related topics (Program, Tulane Univ., New Orleans, La., 1974), Lecture Notes in Math., Vol. 446, Springer, Berlin, (1975)Abstract
In this paper we shall investigate the behavior of
solutions of the semilinear diffusion equation
du/dt = d^2u/dx^2 + f(u)
for large values of the time t. Throughout this work
we shall assume that f(0) : f(1) : 0 and consider only
solutions u(x,t) with values in 0,i . The problems
which we consider are the pure initial value problem in
the half-space ~ × IR + and the initial-boundary value
+ +
problem in the quarter-space IR ×IR
The equation (i.i) occurs in various applications,
and we shall consider forms of the function f(u) which
are suggested by some of these applications.
Description
Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation