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Existence for Parabolic–Elliptic Degenerate Diffusion Problems

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Degenerate Nonlinear Diffusion Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2049))

Abstract

In this chapter we are concerned with the study of some boundary value problems with initial data formulated for parabolic–elliptic degenerate diffusion equations with advection, focusing especially on the fast diffusion case which involves a free boundary problem (case (a) in Introduction).

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References

  1. J.P. Aubin, Un théorème de compacité. C. R. Acad. Sci. Paris Sér. I 256, 5042–5044 (1963)

    MathSciNet  MATH  Google Scholar 

  2. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces (Editura Academiei-Noordhoff International Publishing, Bucureşti-Leyden, 1976)

    Book  MATH  Google Scholar 

  3. V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems (Academic, New York, 1993)

    MATH  Google Scholar 

  4. V. Barbu, Partial Differential Equations and Boundary Value Problems (Kluwer Academic, Dordrecht, 1998)

    MATH  Google Scholar 

  5. V. Barbu, Nonlinear Differential Equations of Monotone Type in Banach Spaces (Springer, New York, 2010)

    Book  Google Scholar 

  6. V. Barbu, A. Favini, Periodic problems for degenerate differential equations. Rend. Istit. Mat. Univ. Trieste Suppl. XXVIII, 29–57 (1997)

    Google Scholar 

  7. V. Barbu, A. Favini, Periodic solutions to degenerate second order differential equations in Hilbert spaces. Commun. Appl. Anal. 2, 19–29 (1998)

    MathSciNet  MATH  Google Scholar 

  8. I. Borsi, A. Farina, R. Gianni, M. Primicerio, Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei 9 Mat. Appl. 20(1), 1–24 (2009)

    Google Scholar 

  9. H. Brezis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert (North-Holland, Amsterdam, 1973)

    MATH  Google Scholar 

  10. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations (Springer, Berlin, 2011)

    MATH  Google Scholar 

  11. P. Broadbridge, I. White, Constant rate rainfall infiltration: A versatile nonlinear model, 1. Analytic solution. Water Resour. Res. 24(1), 145–154 (1988)

    Article  Google Scholar 

  12. C. Ciutureanu, G. Marinoschi, Convergence of the finite difference scheme for a fast diffusion equation in porous media. Numer. Func. Anal. Optim. 29, 1034–1063 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. COMSOL Multiphysics v3.5a. Floating Network License 1025226, Comsol Sweden (2007)

    Google Scholar 

  14. A. Favini, G. Marinoschi, Existence for a degenerate diffusion problem with a nonlinear operator. J. Evol. Equ. 7, 743–764 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Favini, G. Marinoschi, Periodic behavior for a degenerate fast diffusion equation. J. Math. Anal. Appl. 351(2), 509–521 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Granas, J. Dugundji, Fixed Point Theory (Springer, New York, 2003)

    Book  MATH  Google Scholar 

  17. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (Dunod, Paris, 1969)

    MATH  Google Scholar 

  18. J. L. Lions, E. Magenes, Non-homogeneous Boundary Value Problems and Applications, I (Springer, Berlin, 1972)

    Book  Google Scholar 

  19. G. Minty, Monotone (nonlinear) operators in Hilbert spaces. Duke Math. J. 29, 341–346 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  20. G. Marinoschi, Functional approach to nonlinear models of water flow in soils. Mathematical Modelling: Theory and Applications, vol. 21 (Springer, Dordrecht, 2006)

    Google Scholar 

  21. G. Marinoschi, Periodic solutions to fast diffusion equations with non Lipschitz convective terms. Nonlinear Anal. R. World Appl. 10, 1048–1067 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bologna, Bologna, Italy

    Angelo Favini

  2. Romanian Academy Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania

    Gabriela Marinoschi

Authors
  1. Angelo Favini
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  2. Gabriela Marinoschi
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Favini, A., Marinoschi, G. (2012). Existence for Parabolic–Elliptic Degenerate Diffusion Problems. In: Degenerate Nonlinear Diffusion Equations. Lecture Notes in Mathematics, vol 2049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28285-0_1

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