We consider quasilinear parabolic nondiagonal systems of equations with additional terms with quadratic nonlinearity in the gradient. We study the local continuity of solutions that are not necessarily bounded under optimal smoothness conditions on the principal matrix and one-sided conditions on the strongly nonlinear terms.
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Translated from Problemy Matematicheskogo Analiza 116, 2022, pp. 35-58.
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Arkhipova, A.A. Parabolic Systems with Quadratic Nonlinearities in the Gradient. Regularity of Solutions. J Math Sci 264, 525–551 (2022). https://doi.org/10.1007/s10958-022-06015-3
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DOI: https://doi.org/10.1007/s10958-022-06015-3