Geodesic
Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 236-248

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We consider the homogeneous Dirichlet problem for the nonlinear diffusion-absorption equation with a one-sided constraint imposed on diffusion flux values. The family of approximate solutions constructed by means of Alexander Kaplan's integral penalty operator is studied. It is shown that this family converges weakly in the first-order Sobolev space to the solution of the original problem, as the small regularization parameter tends to zero. Thereafter, a property of uniform approximation of solutions is established in Hölder's spaces via systematic study of structure of the penalty operator.
Keywords: penalty method, p-Laplace operator, one-sided constraint.
Mots-clés : diffusion-absorption equation 
@article{SEMR_2019_16_a83,
     author = {T. V. Sazhenkova and S. A. Sazhenkov},
     title = {Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {236--248},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a83/}
}
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T. V. Sazhenkova; S. A. Sazhenkov. Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 236-248. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a83/