In generalized Lebesgue and Sobolev spaces, we consider a mixed problem for a class of parabolic equations with double nonlinearity and nondegenerate minor terms whose exponents of nonlinearity are functions of the space variables. By using the Galerkin method, we establish the conditions of existence of weak solutions of the posed problem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 5, pp. 612–628, May, 2011.
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Bokalo, T.M., Buhrii, O.M. Doubly nonlinear parabolic equations with variable exponents of nonlinearity. Ukr Math J 63, 709–728 (2011). https://doi.org/10.1007/s11253-011-0537-5
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DOI: https://doi.org/10.1007/s11253-011-0537-5