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On Bounded Solutions for Nonlinear Parabolic Equations with Degenerate Coercivity

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Abstract

By means of Stampacchia’s lemma, we prove an existence result of bounded solutions for some nonlinear parabolic equations with degenerate coercivity.

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References

  1. Alvino A., Boccardo L., Ferone V., Orsina L., Trombetti G.: Existence results for nonlinear elliptic equations with degenerate coercivity. Ann. Mat. Pura Appl. (4) 182(1), 53–79 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benkirane A., Youssfi A.: Regularity for solutions of nonlinear elliptic equations with degenerate coercivity. Ric. Mat. 56(2), 241–275 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Boccardo, L., Dall’Aglio, A., Gallouët, T., Orsina, L.: Existence and regularity results for some nonlinear parabolic equations. Adv. Math. Sci. Appl. 9(2), 1017–1031 (1999)

  4. Cirmi, G.R., Porzio, M.M.: \({L^{\infty}}\)-Solutions for some nonlinear degenerate elliptic and parabolic equations. Ann. Mat. Pura Appl. (IV) CLXIX, 67–86 (1995)

  5. Della Pietra F., di Blasio G.: Existence and comparison results for non-uniformly parabolic problems. Mediterr. J. Math. 7, 323–340 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Li F.: Existence and regularity results for some parabolic equations with degenerate coercivity. Ann. Acad. Sci. Fenn. Math. 37, 605–633 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lions J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969)

    MATH  Google Scholar 

  8. Nirenberg L.: On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa. 13, 116–162 (1959)

    MathSciNet  MATH  Google Scholar 

  9. Porzio M.M., Pozio M.A.: Parabolic equations with non-linear degenerate and space-time dependent operators. J. Evol. Equ. 8, 31–70 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Simon J.: Compact sets in the space L p(0,T;B). Ann. Mat. Pura Appl. 146, 65–96 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  11. Stampacchia G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Ist. Fourier (Grenoble) 15, 189–258 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhou S.L.: A priori \({L^{\infty}}\)-estimate and existence of solutions for some nonlinear parabolic equations. Nonlinear Anal. 42, 887–904 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Engineering, Systems and Applications, National School of Applied Sciences, University Sidi Mohamed Ben Abdellah, P.O. Box 72, Fès-Principale, Fès, Morocco

    Ahmed Youssfi

  2. Laboratory of Mathematical Analysis and Applications, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P.O. Box 1796, Atlas, Fès, Morocco

    Abdelmoujib Benkirane & Youssef El Hadfi

Authors
  1. Ahmed Youssfi
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  2. Abdelmoujib Benkirane
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  3. Youssef El Hadfi
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Correspondence to Ahmed Youssfi.

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Youssfi, A., Benkirane, A. & El Hadfi, Y. On Bounded Solutions for Nonlinear Parabolic Equations with Degenerate Coercivity. Mediterr. J. Math. 13, 3029–3040 (2016). https://doi.org/10.1007/s00009-015-0670-8

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  • DOI: https://doi.org/10.1007/s00009-015-0670-8

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