A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation
Abbreviated Journal Title
Nonlinear Anal.-Real World Appl.
Nagumo reaction-diffusion equation; Nagumo telegraph equation; Numerical; solution; Mathematics, Applied
We consider the Nagumo reaction-diffusion equation u(t) = u(xx) + f(u) and the Nagumo telegraph equation tau u(tt) + (1 - tau f'(u))u(t) = u(xx) + f(u), where f(u) = u(a - u)(1 - u) as boundary value problems over the finite spatial interval x is an element of [0, L] and finite time t is an element of [0, t*]. We are able to obtain approximate solutions for the boundary value problems via a variational technique. Also, we obtain numerical solutions for some special cases, in order to demonstrate the validity of the variational technique. Also, these numerical solutions are used to discuss the qualitative characteristics of the solutions for the specific initial data considered. (C) 2009 Elsevier Ltd. All rights reserved.
Nonlinear Analysis-Real World Applications
"A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation" (2010). Faculty Bibliography 2010s. 892.