On the computation of the quenching time for a nonlinear diffusion equation with singular boundary outfluxes
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This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation $(u^{m})_t=u_{xx}$, $0<x<1, t>0$, with a singular boundary outfluxes $u_x(0,t)=u^{-p}(0,t)$, $u_x(1,t)=-u^{-q}(1,t)$, $t>0$. We use the finite differences method to obtain a semidiscrete scheme of the above problem. First, we give appropriate conditions under which the semidiscrete solution quenches in a finite time and estimate its semidiscrete quenching time. Then, we establish the convergence of the semidiscrete quenching time. Finally, we illustrate our analysis with some numerical experiments.
Abstract
This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation $(u^{m})_t=u_{xx}$, $0<x<1, t>0$, with a singular boundary outfluxes $u_x(0,t)=u^{-p}(0,t)$, $u_x(1,t)=-u^{-q}(1,t)$, $t>0$. We use the finite differences method to obtain a semidiscrete scheme of the above problem. First, we give appropriate conditions under which the semidiscrete solution quenches in a finite time and estimate its semidiscrete quenching time. Then, we establish the convergence of the semidiscrete quenching time. Finally, we illustrate our analysis with some numerical experiments.
참고문헌 (12)
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