Abstract
For a linearized finite-difference scheme approximating the Dirichlet problem for a multidimensional quasilinear parabolic equation with unbounded nonlinearity, we establish pointwise two-sided solution estimates consistent with similar estimates for the differential problem. These estimates are used to prove the convergence of finite-difference schemes in the grid L 2 norm.
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Original Russian Text © P.P. Matus, D.B. Poliakov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 7, pp. 991–1000.
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Matus, P.P., Poliakov, D.B. Consistent two-sided estimates for the solutions of quasilinear parabolic equations and their approximations. Diff Equat 53, 964–973 (2017). https://doi.org/10.1134/S0012266117070126
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DOI: https://doi.org/10.1134/S0012266117070126