Abstract
This paper deals with the study of the numerical approximation for the following semilinear equation with a nonlinear absorption term ut = uxx− λup, 0 < x < 1, t > 0, and a nonlinear flux boundary condition ux(0,t) = 0, ux(1,t) = uq(1,t), t > 0. We give conditions under which the positive semidiscrete solution blows up in a finite time. Convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero is established. Finally, we use an efficient algorithm to estimate the blow-up time.
Highlights
Consider the following semilinear parabolic problem uuut(xx(=0,0ut))xx==−u00λ,(uxup)x,(>1,00t,) 1, 0 t > (1)where p, q > 1, λ > 0 are u′0(1) = uq0(1)
This paper deals with the study of the numerical approximation for the following semilinear equation with a nonlinear absorption term ut = uxx − λup, 0 < x < 1, t > 0, and a nonlinear flux boundary condition ux(0, t) = 0, ux(1, t) = uq(1, t), t > 0
For differential equations, solutions can become unbounded in finite time, we say that they blow up, or they can be defined for all time and we call them global solutions
Summary
Consider the following semilinear parabolic problem uuut(xx(=0, ,0ut))xx==−u00λ,(uxup)x,(>1,00t,)
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