We establish the unique solvability of the first boundary value problem for a semilinear second order parabolic equation with varying time direction by using a modified Galerkin method and the regularization method. We obtain a priori error estimates for approximate solutions.
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E. S. Efimova, I. E. Egorov, and M. S. Kolesova, “Error estimate for the stationary Galerkin method applied to a semilinear parabolic equation with alternating time direction,” J. Math. Sci., New York 213, No. 6, 838–843 (2016).
Yu. A. Dubinskii, “Quasilinear elliptic and parabolic equations of arbitrary order” [in Russian], Usp. Mat. Nauk 23, No. 1, 45–90 (1968).
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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 16, No. 2, 2016, pp. 6-15.
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Egorov, I.E., Efimova, E.S. Galerkin Method for Semilinear Parabolic Equation with Varying Time Direction. J Math Sci 228, 372–379 (2018). https://doi.org/10.1007/s10958-017-3628-5
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DOI: https://doi.org/10.1007/s10958-017-3628-5