Geodesic
To nonlocal boundary value problems for a multidimensional parabolic equation with variable coefficients
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2019), pp. 107-122

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The paper studies nonlocal boundary value problems for a parabolic equation with variable coefficients in a multidimensional domain. Studies of the set nonlocal boundary value problems are carried out assuming the existence of a regular solution. To solve the corresponding differential problem under consideration by the method of energy inequalities, a priori estimates in the differential and difference interpretations are obtained. From the obtained a priori estimates the uniqueness and stability of the solution on the right side and the initial data, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem at a rate of $O(|h|+\tau)$, follow.
Mots-clés : a priori estimation, parabolic equation, nonlocal condition.
Keywords: multidimensional equation, difference scheme, stability and convergence of difference schemes 
@article{VTPMK_2019_2_a6,
     author = {Z. V. Beshtokova},
     title = {To nonlocal boundary value problems for a multidimensional parabolic equation with variable coefficients},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {107--122},
     publisher = {mathdoc},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2019_2_a6/}
}
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Z. V. Beshtokova. To nonlocal boundary value problems for a multidimensional parabolic equation with variable coefficients. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2019), pp. 107-122. http://geodesic.mathdoc.fr/item/VTPMK_2019_2_a6/