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Existence for some quasilinear elliptic systems with critical growth nonlinearity and L 1 data

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove the existence of weak solutions for some quasilinear elliptic reaction-diffusion systems with Dirichlet boundary conditions and satisfying to the two main properties: the positivity of the solutions and the balance law. The nonlinearity we consider here has critical growth with respect to the gradient and data are in L1.
Słowa kluczowe
Wydawca
Rocznik
Strony
81--94
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Faculté des Sciences et Techniques Gueliz, Departement de Mathématiques et Informatique, B. P. 618 Marrakech, Maroc
autor
  • Faculté des Sciences et Techniques Gueliz, Departement de Mathématiques et Informatique, B. P. 618 Marrakech, Maroc
autor
  • Universitě Cadi Ayyad, Faculté des Sciences Semlalia, Departement de Mathématiques, Prince My Abdellah B. P. 511, Marrakech, Maroc
Bibliografia
  • [1] Alaa, N., Solutions faibles d'equations paraboliques quasi-linéaires avec données initiales mesures, Ann. Math. Blaise Pascal 3(2) (1996), 1-15.
  • [2] Alaa, N., Mounir, I., Global existence for reaction-diffusion systems with mass control and critical growth with respect to the gradient, J. Math. Anal. Appl. 253 (2001), 532-557.
  • [3] Alaa, N., Mounir, I., Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient, Ann. Math. Blaise Pascal 8(2) (2001), 1-19.
  • [4] Alaa, N., Pierre, M., Weak solution of some quasilinear elliptic equations with measures, SIAM J. Math. Anal. 24(1) (1993), 23-35.
  • [5] Amann, H., Crandall, M. G., On some existence theorems for semi linear equations, Indiana Univ. Math. J. 27 (1978), 779-790.
  • [6] Bensoussan, A., Boccardo, L., Murat, F., On a non linear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. H. Poincare Anal. Non Linéaire 5(4) (1988), 347-364.
  • [7] Boccardo, L., Murat, F., Puel, J. P., Existence de solutions non bornées pour certaines équations quasi-linéaires, Portugal. Math. 41 (1982), 507-534.
  • [8] Boudiba, N., Existence globale pour des systèmes de reaction-diffusion avec controle de masse, Ph.D. thesis, Universite de Rennes I, France, 1999.
  • [9] Brezis, H., Strauss, W., Semilinear elliptic equation in L1, J. Math. Soc. Japan 25 (1973), 565-590.
  • [10] Choquet-Bruhat, Y., Leray, J., Sur le probléme de Dirichlet quasilinéaire d'ordre deux, C. R. Acad. Sci. Paris Ser. I Math. 274 (1972), 81-85.
  • [11] Fitzgibbon, W. E., Morgan, J., Existence of solutions for a class of weakly coupled semilinear elliptic systems, J. Differential Equations 77 (1989), 351-368.
  • [12] Fitzgibbon, W. E., Morgan, J., Sanders, R., Global existence and boundedness for class of inhomogeneous semilinear parabolic systems, Nonlinear Anal. 19(9) (1992), 885-899.
  • [13] Hollis, S. L., Martin, R. H., Pierre, M., Global existence and boundeness in reaction-diffusion systems, SIAM. J. Math. Anal. 18 (1987), 744-761.
  • [14] Lions, P. L., Resolution de problěmes elliptiques quasilinéaires, Arch. Rational Mech. Anal. 74 (1980), 335-353.
  • [15] Lions, J. L., Quelques méthodes de resolutions des problěmes aux limites non linéaires, Dunod; Gauthier Villars, Paris, 1969.
  • [16] Maach, F., Existence pour des systěmes de reaction-diffusion quasi-linéaires avec loi de balance, Ph.D. thesis, Universitě Henri Poincare, Nancy I, France, 1994.
  • [17] Pierre, M., An L1 -method to prove global existence in some reaction-diffusion systems, in „Contribution to Nonlinear Partial Differential Equations”, Vol. II (Paris, 1985), Pitman Res. Notes Math. Ser. 155 (1987), 220-231.
  • [18] Pierre, M., Schmitt, D., Blow up in reaction-diffusion systems with dissipation of mass, SIAM J. Math. Anal. 28(2) (1987), 259-269.
  • [19] Pierre, M., Schmitt, D., Blow up in reaction-diffusion systems with dissipation of mass, SIAM Rev. 42(1) (2000), 93-106.
  • [20] Porretta, A., Existence for elliptic equations in L1 having lower order terms with natural growth, Portugal. Math. 57(2) (2000), 179-190.
  • [21] Rothe, F., Global Solutions of Reaction-Diffusion Systems, Lectures Notes in Math. 1072 (1984), Springer, New York.
  • [22] Schwartz, J. T., Nonlinear Functional Analysis, Gordon and Breach Science Publishers, New York-London, Paris, 1969.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD4-0001-0017
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