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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper concerns the study of the numerical approximation for the following boundary value problem: $$ \cases u_t(x,t)-u_{xx}(x,t) = -u^{-p}(x,t), 00, \ u_{x}(0,t)=0, u(1,t)=1, t>0, \ u(x,0)=u_{0}(x)>0, 0\leq x \leq 1, \endcases $$ 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.
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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     author = {Nabongo, Diabate and Boni, Th\'eodore K.},
     title = {Quenching for semidiscretizations of a semilinear heat equation with {Dirichlet} and {Neumann} boundary conditions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {463--475},
     year = {2008},
     volume = {49},
     number = {3},
     mrnumber = {2490440},
     zbl = {1212.35217},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_3_a7/}
}
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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/