Geodesic
Quenching for semidiscretizations of a semilinear heat equation with Dirichlet and Neumann boundary conditions
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 3, pp. 463-475.

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This paper concerns the study of the numerical approximation for the following boundary value problem: $$ \cases u_t(x,t)-u_{xx}(x,t) = -u^{-p}(x,t), 01, t>0, \ u_{x}(0,t)=0, u(1,t)=1, t>0, \ u(x,0)=u_{0}(x)>0, 0\leq x \leq 1, \endcases $$ where $p>0$. We obtain some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time. Finally, we give some numerical experiments to illustrate our analysis.
Classification : 35B40, 35K20, 35K55, 35K91, 65M06
Keywords: semidiscretizations; discretizations; heat equations; quenching; semidiscrete quenching time; convergence 
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     title = {Quenching for semidiscretizations of a semilinear heat equation with {Dirichlet} and {Neumann} boundary conditions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Nabongo, Diabate; Boni, Théodore K. Quenching for semidiscretizations of a semilinear heat equation with Dirichlet and Neumann boundary conditions. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 3, pp. 463-475. http://geodesic.mathdoc.fr/item/CMUC_2008__49_3_a7/