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An existence result for a solution of a class of nonlinear parabolic equations in Orlicz spaces is established. The data belongs to L1, no growth assumption is made on the nonlinearities and the N-function does not satisfy the Δ2 condition.
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Elhoussine Azroul, Hicham Redwane, Mohamed Rhoudaf, Existence of a renormalized solution for a class of nonlinear parabolic equations in Orlicz spaces. Port. Math. 66 (2009), no. 1, pp. 29–63