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In this paper we prove existence and uniqueness of weak solutions to nonlinear parabolic problems with variable exponent with Neumann-type boundary conditions. Our approach is based essentially on time discretization technique by Euler forward scheme. Mathematics Subject Classification: 35B35, 35D30, 35K55, 35J62doi:10.12988/ijma.2016.6223 fatcat:74553vy3zbeuvfz65xolyja3xq