ASYMPTOTIC BEHAVIOR FOR NUMERICAL SOLUTIONS OF A SEMILINEAR PARABOLIC EQUATION WITH A NONLINEAR BOUNDARY CONDITION

This paper concerns the study of the numerical approximation for the following initial-boundary value problem, u(t) = u(xx) - au(p), 0 < x < 1, t > 0, u(x)(0,t) = 0, u(x)(1,t) + bu(q)(1,t) = 0, t > 0, u(x,0) = u(0)(x)>= 0, 0 <= x <= 1, where a > 0, b > 0 and p > q > 1. We show that the solution of a semidiscrete form of the initial value problem above goes to zero as t approaches infinity and give its asymptotic behavior. We provide some numerical experiments that illustrate our analysis.