Nonlinear parabolic equations with p-growth and unbounded data |
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| Institution: | 1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy;2. Département de mathématiques, Université de Poitiers, 40, avenue du Recteur-Pineau, 86022 Poitiers, France;3. L3MA, SP2MI, boulevard 3, Téléport 2, B.P. 179, 86960 Futuroscope, France;1. Section de Mathématiques, École Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland;2. Dipartimento di Scienze di Base e Applicate per l’ Ingegneria, “Sapienza” Università di Roma, Via Scarpa 16, 00161 Roma, Italy;1. Department of Mathematics, Osaka City University, Sumiyoshi-ku, Osaka, 558-8585, Japan;2. OCAMI, Sumiyoshi-ku, Osaka, 558-8585, Japan;1. Novgorod State University, 41, B. St-Petersburgskaya str., Veliky Novgorod, 173003, Russian Federation;2. Peoples'' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation |
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| Abstract: | The purpose of this paper is to prove the existence of a solution for a nonlinear parabolic equation in the form ut - div(a(t, x, u, Du)) = H(t, x, u, Du) - div(g(t, x)) in QT =]0,T×Ω, Ω ⊂ RN, with an initial condition u(0) = u0, where u0 is not bounded, |H(t,x, u, ξ)⩽ β|ξ|p + f(t,x) + βeλ1|u|f, |g|p/(p-1) ∈ Lr(QT) for some r = r{N) ⩾ 1, and - div(a(t,x,u, Du)) is the usual Leray-Lions operator. |
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