Existence of a Renormalized Solution of a Parabolic Problem in Anisotropic Sobolev–Orlicz Spaces - Vorob’yov, N. A.; Mukminov, F. Kh (Journal of mathematical sciences (New York, N.Y.), 2021)
We consider the first mixed problem for a certain class of anisotropic parabolic equations of the form β x u t ′ − div a t x u ∇ u − b t x u ∇ u = u where μ is a measure and the coefficients contain nonpower nonlinearities in the cylindrical domain D T = (0 , T ) × Ω, where Ω ⊂ ℝ n is a bounded domain. We prove the existence of a renormalized solution of the problem for g t = 0 and a function β ( x, r ), which increases with respect to r and satisfies the Carath´eodory condition.