We study the problem of boundedness of weak solutions of a general nondiagonal parabolic system of nonlinear differential equations whose matrix of coefficients satisfies special structural conditions. To do this, we use a procedure based on the estimation of a certain function of unknowns.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 3, pp. 400–407, March, 2009.
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Portnyahin, D.V. Boundedness of weak solutions of a nondiagonal parabolic system of two equations. Ukr Math J 61, 478–489 (2009). https://doi.org/10.1007/s11253-009-0213-1
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DOI: https://doi.org/10.1007/s11253-009-0213-1