Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data

References

[1] Akdim Y., Benkirane A. and El Moumni M., Solutions of nonlinear elliptic problems with lower order terms, Ann. Funct. Anal. 6 (2015), no. 1, 34–53. 10.15352/afa/06-1-4Suche in Google Scholar

[2] Akdim Y., Benkirane A., El Moumni M. and Redwane H., Existence of renormalized solutions for nonlinear parabolic equations, J. Partial Differ. Equ. 27 (2014), no. 1, 28–49. 10.4208/jpde.v27.n1.2Suche in Google Scholar

[3] Akdim Y., Bennouna J., Mekkour M. and Redwane H., Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities, Appl. Math. (Warsaw) 39 (2012), no. 1, 1–22. 10.4064/am39-1-1Suche in Google Scholar

[4] Alvino A. and Trombetti G., The best majorization constants for a class of degenerate elliptic equations (in Italian), Ric. Mat. 27 (1978), no. 2, 413–428. Suche in Google Scholar

[5] Beckenbach E.-F. and Bellman R., Inequalities, 2nd rev. printing, Ergeb. Math. Grenzgeb. (2) 30, Springer, New York, 1965. 10.1007/978-3-662-35199-4Suche in Google Scholar

[6] Bénilan P., Boccardo L., Gallouët T., Gariepy R., Pierre M. and Vázquez J. L., An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 22 (1995), no. 2, 241–273. Suche in Google Scholar

[7] Blanchard D. and Murat F., Renormalised solutions of nonlinear parabolic problems with L1 data: Existence and uniqueness, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), no. 6, 1137–1152. 10.1017/S0308210500026986Suche in Google Scholar

[8] Blanchard D., Murat F. and Redwane H., Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems, J. Differential Equations 177 (2001), no. 2, 331–374. 10.1006/jdeq.2000.4013Suche in Google Scholar

[9] Blanchard D. and Redwane H., Existence of a solution for a class of parabolic equations with three unbounded nonlinearities, natural growth terms and L1 data, Arab J. Math. Sci. 20 (2014), no. 2, 157–176. 10.1016/j.ajmsc.2013.06.002Suche in Google Scholar

[10] Boccardo L., Dall’Aglio A., Gallouët T. and Orsina L., Nonlinear parabolic equations with measure data, J. Funct. Anal. 147 (1997), no. 1, 237–258. 10.1006/jfan.1996.3040Suche in Google Scholar

[11] Boccardo L. and Gallouët T., Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989), no. 1, 149–169. 10.1016/0022-1236(89)90005-0Suche in Google Scholar

[12] Boccardo L., Giachetti D., Diaz J. I. and Murat F., Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms, J. Differential Equations 106 (1993), no. 2, 215–237. 10.1006/jdeq.1993.1106Suche in Google Scholar

[13] Dal Maso G., Murat F., Orsina L. and Prignet A., Definition and existence of renormalized solutions of elliptic equations with general measure data, C. R. Math. Acad. Sci. Paris 325 (1997), no. 5, 481–486. 10.1016/S0764-4442(97)88893-3Suche in Google Scholar

[14] Dall’Aglio A. and Orsina L., Nonlinear parabolic equations with natural growth conditions and L1 data, Nonlinear Anal. 27 (1996), no. 1, 59–73. 10.1016/0362-546X(94)00363-MSuche in Google Scholar

[15] Di Nardo R., Nonlinear parabolic equations with a lower order term and L1 data, Commun. Pure Appl. Anal. 9 (2010), no. 4, 929–942. 10.3934/cpaa.2010.9.929Suche in Google Scholar

[16] Di Nardo R., Feo F. and Guibé O., Existence result for nonlinear parabolic equations with lower order terms, Anal. Appl. (Singap.) 9 (2011), no. 2, 161–186. 10.1142/S0219530511001790Suche in Google Scholar

[17] DiPerna R. J. and Lions P.-L., On the Cauchy problem for Boltzmann equations: Global existence and weak stability, Ann. of Math. (2) 130 (1989), no. 2, 321–366. 10.2307/1971423Suche in Google Scholar

[18] Hardy G. H., Littlewood J. E. and Polya G., Inequalities, Cambridge University Press, Cambridge, 1964. Suche in Google Scholar

[19] Landes R., On the existence of weak solutions for quasilinear parabolic initial-boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), no. 3–4, 217–237. 10.1017/S0308210500020242Suche in Google Scholar

[20] Lions J.-L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. Suche in Google Scholar

[21] Lions P.-L., Mathematical Topics in Fluid Mechanics. Vol. 1: Incompressible Models, Oxford Lecture Ser. Math. Appl. 3, Clarendon Press, Oxford, 1996. Suche in Google Scholar

[22] Monetti V. M. and Randazzo L., Existence results for nonlinear elliptic equations with p-growth in the gradient, Ric. Mat. 49 (2000), no. 1, 163–181. Suche in Google Scholar

[23] Murat F., Soluciones renormalizadas de EDP elipticas non lineales, Cours à l’Université de Séville, Publication R93023, Laboratoire d’Analyse Numérique, Paris VI, Paris, 1993. Suche in Google Scholar

[24] Murat F., Équations elliptiques non linéaires avec second membre L1 ou mesure, Comptes Rendus du 26ème Congrès National d’Analyse Numérique (Les Karellis 1994), Université de Lyon, Lyon (1994), A12–A24. 10.5802/jedp.538Suche in Google Scholar

[25] Porretta A., Existence results for nonlinear parabolic equations via strong convergence of truncations, Ann. Mat. Pura Appl. (4) 177 (1999), 143–172. 10.1007/BF02505907Suche in Google Scholar

[26] Porretta A., Nonlinear equations with natural growth terms and measure data, Electron. J. Differ. Equ. Conf. 9 (2002), 183–202. Suche in Google Scholar

[27] Porzio M. M., Existence of solutions for some “noncoercive” parabolic equations, Discrete Contin. Dynam. Systems 5 (1999), no. 3, 553–568. 10.3934/dcds.1999.5.553Suche in Google Scholar

[28] Rakotoson J.-M., Uniqueness of renormalized solutions in a T-set for the L1-data problem and the link between various formulations, Indiana Univ. Math. J. 43 (1994), no. 2, 685–702. 10.1512/iumj.1994.43.43029Suche in Google Scholar

[29] Redwane H., Solution renormalises de problè,mes paraboliques et elleptique non linéaires, Ph. D. thesis, Rouen, 1997. Suche in Google Scholar

[30] Redwane H., Existence of a solution for a class of parabolic equations with three unbounded nonlinearities, Adv. Dyn. Syst. Appl. 2 (2007), no. 2, 241–264. Suche in Google Scholar

[31] Redwane H., Existence results for a class of nonlinear parabolic equations in Orlicz spaces, Electron. J. Qual. Theory Differ. Equ. 2010 (2010), Article ID 2. 10.14232/ejqtde.2010.1.2Suche in Google Scholar

[32] Youssfi A., Benkirane A. and El Moumni M., Existence result for strongly nonlinear elliptic unilateral problems with L1-data, Complex Var. Elliptic Equ. 59 (2014), no. 4, 447–461. 10.1080/17476933.2012.725166Suche in Google Scholar