Asymptotic Analysis of the $p$-Laplacian Flow in an Exterior Domain

Iagar, Razvan Gabriel; VáZquez, Juan Luis

doi:10.1016/j.anihpc.2007.11.004

Asymptotic Analysis of the

p

-Laplacian Flow in an Exterior Domain

Iagar, Razvan Gabriel ; VáZquez, Juan Luis

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 497-520

Zbl

DOI : 10.1016/j.anihpc.2007.11.004

@article{AIHPC_2009__26_2_497_0,
     author = {Iagar, Razvan Gabriel and V\'aZquez, Juan Luis},
     title = {Asymptotic {Analysis} of the $p${-Laplacian} {Flow} in an {Exterior} {Domain}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {497--520},
     year = {2009},
     publisher = {Elsevier},
     volume = {26},
     number = {2},
     doi = {10.1016/j.anihpc.2007.11.004},
     zbl = {1178.35070},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.11.004/}
}

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Iagar, Razvan Gabriel; VáZquez, Juan Luis. Asymptotic Analysis of the $p$-Laplacian Flow in an Exterior Domain. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 497-520. doi: 10.1016/j.anihpc.2007.11.004

Bibliographie
Cité par

[1] Abdellaoui B., Peral I., Existence and Nonexistence Results for Quasilinear Elliptic Equations Involving the P-Laplacian With a Critical Potential, Ann. Mat. Pura Appl. 182 (3) (2003) 247-270. | MR

[2] Brandle C., Quirós F., Vázquez J. L., Asymptotic Behaviour of the Porous Media Equation in Domains With Holes, Interfaces and Free Boundaries 9 (2007) 211-233. | Zbl | MR

[3] Diaz J. I., Saa E., Existence Et Unicité De Solutions Positives Pour Certaines Équations Elliptiques Quasilinéaires, C. R. Acad. Sci. Paris Sér. I Math. 307 (12) (1987) 521-524, (in French). | Zbl | MR

[4] Dibenedetto E., Degenerate Parabolic Equations, Series Universitext, Springer-Verlag, New York, 1993. | Zbl | MR

[5] Esteban J. R., Vázquez J. L., Homogeneous Diffusion in R With Power-Like Nonlinear Diffusivity, Arch. Rat. Mech. Anal. 103 (1) (1988) 39-80. | Zbl | MR

[6] Galaktionov V., Vázquez J. L., A Stability Technique for Evolution Partial Differential Equations. a Dynamical System Approach, Progress in Nonlinear Differential Equations and Their Applications, vol. 56, Birkhäuser, 2004. | Zbl | MR

[7] Galaktionov V., Vázquez J. L., Asymptotic Behaviour of Nonlinear Parabolic Equations With Critical Exponents. a Dynamical System Approach, J. Funct. Anal. 100 (2) (1991) 435-462. | Zbl | MR

[8] Gilbarg D., Trudinger N. S., Elliptic Partial Differential Equations of Second Order, Classics in Mathematics, Springer-Verlag, Berlin, 2002. | Zbl | MR

[9] Gilding B., Gonzerkiewicz J., Localization of Solutions of Exterior Domain Problems for the Porous Media Equation With Radial Symmetry, SIAM J. Math. Anal. 31 (2000) 862-893. | Zbl | MR

[10] B. Gilding, J. Gonzerkiewicz, Large time behaviour of solutions of the exterior-domain Cauchy-Dirichlet problem for the porous media equation with homogeneous boundary data, Preprint, 2005. | Zbl | MR

[11] Iagar R., Sánchez A., Vázquez J. L., Radial Equivalence for the Two Basic Nonlinear Degenerate Diffusion Equations, J. Math. Pures Appl. 89 (1) (2008) 1-24. | Zbl | MR

[12] R. Iagar, J.L. Vázquez, Anomalous large-time behaviour of the p-Laplacian flow in an exterior domain in low dimension, Preprint, 2008. | MR

[13] Ishige K., Movement of Hot Spots on the Exterior Domain of a Ball Under the Neumann Boundary Condition, J. Differential Equations 212 (2) (2005) 394-431. | Zbl | MR

[14] K. Ishige, Movement of hot spots on the exterior domain of a ball, Preprint.

[15] Kamin S., Vázquez J. L., Fundamental Solutions and Asymptotic Behaviour for the P-Laplacian Equation, Rev. Mat. Iberoamericana 4 (2) (1988) 339-354. | Zbl | MR

[16] Kamin S., Vázquez J. L., Asymptotic Behaviour of Solutions of the Porous Medium Equations With Changing Sign, SIAM J. Math. Anal. 22 (1) (1991) 34-45. | Zbl | MR

[17] Quirós F., Vázquez J. L., Asymptotic Behaviour of the Porous Medium Equation in an Exterior Domain, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (4) (1999) 183-227. | Zbl | MR | Numdam

[18] Vázquez J. L., Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type, Oxford University Press, Oxford, 2006. | Zbl | MR

[19] Vázquez J. L., Asymptotic Behaviour for the Porous Medium Equation Posed in the Whole Space, J. Evol. Equations 3 (1) (2003) 67-118, Dedicated to Philippe Benilan. | Zbl | MR

[20] Vázquez J. L., The Porous Medium Equation. Mathematical Theory, Oxford Mathematical Monographs, Oxford University Press, 2007. | Zbl | MR

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