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Initial trace of positive solutions of a class of degenerate heat equation with absorption
1. | Department of Mathematics, Technion, 32000 Haifa, Israel |
2. | Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Université François Rabelais, Tours, France |
References:
[1] |
G. I. Barenblatt, On self-similar motions of compressible fluids in porous media, Prikl. Mat. Mech., 16 (1952), 679-698 (Russian) |
[2] |
M. F. Bidaut-Véron, E. Chasseigne and L. Véron, Initial trace of solution of some quasilinear parabolic equations with absorption, J. Funct. Anal., 193 (2002), 140-205.
doi: 10.1006/jfan.2002.3912. |
[3] |
X. Chen, Y. Qi and M. Wang, Singular solution of the parabolic p-Laplacian with absorption, Trans. Amer. Math. Soc., 359 (2007), 5653-5668.
doi: 10.1090/S0002-9947-07-04336-X. |
[4] |
M. G. Crandall and T. A. Liggett, Generation of seigroups of nonlinear transformations in general Banach spaces, Amer. J. Math., 93 (1971), 265-298. |
[5] |
E. DiBenedetto, "Degenerate Parabolic Equations," Springer-Verlag, Series Universitext, New York, 1993.
doi: 10.1007/978-1-4612-0895-2. |
[6] |
E. DiBenedetto and M. A. Herrero, Non-negative solutions of the evolution p-Laplacian equation. Initial traces and cauchy problem when $1 < p < 2$, Arch. Rat. Mech. Anal., 111 (1990), 225-290.
doi: 10.1007/BF00400111. |
[7] |
A. Friedman and L. Véron, Singular solutions of some quasilinear elliptic equations, Arch. Rat. Mech. Anal., 96 (1986), 359-387.
doi: 10.1007/BF00251804. |
[8] |
M. Guedda and L. Véron, Local and global properties of solutions of quasilinear elliptic equations, J. Differential Equations, 76 (1988), 159-189.
doi: 10.1016/0022-0396(88)90068-X. |
[9] |
M. Herrero and J. L. Vazquez, Asymptotic behaviour of the solution of a strongly nonlinear parabolic problem, Ann. Fac. Sci. Toulouse (5)ème serie, 3 (1981), 113-127. |
[10] |
S. Kamin and J. L. Vazquez, Fundamental solutions and asymptotic behaviour for the p-Laplacian equation, Rev. Mat. Iberoamericana, 4 (1988), 339-352.
doi: 10.4171/RMI/77. |
[11] |
S. Kamin and J. L. Vazquez, Singular solutions of of some nonlinear parabolic equations, J. Analyse Math., 59 (1992), 51-74.
doi: 10.1007/BF02790217. |
[12] |
J. B. Keller, On solutions of $\Delta u=f(u)$, Comm. Pure Appl. Math., 10 (1957), 503-510. |
[13] |
F. Li, Regularity for entropy solutions of a class of parabolic equations with irregular data, Comment. Math. Univ. Carolin., 48 (2007), 69-82. |
[14] |
M. Marcus and L. Véron, Initial trace of positive solutions to semilinear parabolic inequalities, Adv. Nonlinear Studies, 2 (2002), 395-436. |
[15] |
T. Nguyen Phuoc and L. Véron, Local and global properties of solutions of heat equation with superlinear absorption, Adv. Differential Equations, 16 (2011), 487-522. |
[16] |
S. Segura de Leon and J. Toledo, Regularity for entropy solutions of parabolic p-Laplacian type equations, Publicacions Matemàtiques, 43 (1999), 665-683.
doi: 10.5565/PUBLMAT_43299_08. |
[17] |
J. L. Vazquez, An a priori interior estimate for the solutions of a nonlinear problem representing weak diffusion, Nonlinear Anal., 5 (1981), 95-103.
doi: 10.1016/0362-546X(81)90074-2. |
[18] |
J. L. Vazquez and L. Véron, Isolated singularities of some semilinear elliptic equations, J. Differential Equations, 60 (1985), 301-321.
doi: 10.1016/0022-0396(85)90127-5. |
[19] |
J. L. Vazquez and L. Véron, Different kinds of singular solutions of nonlinear parabolic equations, Nonlinear Problems in Applied Mathematics, 240-249, SIAM, Philadelphia, PA, (1996). |
[20] |
L. Véron, Some remarks on the convergence of approximate solutions of nonlinear evolution equations in Hilbert spaces, Math. Comp., 39 (1982), 325-337.
doi: 10.2307/2007318. |
[21] |
L. Véron, "Singularities of Solutions of Second Other Quasilinear Equations," Pitman Research Notes in Math. Series 353, Adison Wesley, Longman, 1996. |
show all references
References:
[1] |
G. I. Barenblatt, On self-similar motions of compressible fluids in porous media, Prikl. Mat. Mech., 16 (1952), 679-698 (Russian) |
[2] |
M. F. Bidaut-Véron, E. Chasseigne and L. Véron, Initial trace of solution of some quasilinear parabolic equations with absorption, J. Funct. Anal., 193 (2002), 140-205.
doi: 10.1006/jfan.2002.3912. |
[3] |
X. Chen, Y. Qi and M. Wang, Singular solution of the parabolic p-Laplacian with absorption, Trans. Amer. Math. Soc., 359 (2007), 5653-5668.
doi: 10.1090/S0002-9947-07-04336-X. |
[4] |
M. G. Crandall and T. A. Liggett, Generation of seigroups of nonlinear transformations in general Banach spaces, Amer. J. Math., 93 (1971), 265-298. |
[5] |
E. DiBenedetto, "Degenerate Parabolic Equations," Springer-Verlag, Series Universitext, New York, 1993.
doi: 10.1007/978-1-4612-0895-2. |
[6] |
E. DiBenedetto and M. A. Herrero, Non-negative solutions of the evolution p-Laplacian equation. Initial traces and cauchy problem when $1 < p < 2$, Arch. Rat. Mech. Anal., 111 (1990), 225-290.
doi: 10.1007/BF00400111. |
[7] |
A. Friedman and L. Véron, Singular solutions of some quasilinear elliptic equations, Arch. Rat. Mech. Anal., 96 (1986), 359-387.
doi: 10.1007/BF00251804. |
[8] |
M. Guedda and L. Véron, Local and global properties of solutions of quasilinear elliptic equations, J. Differential Equations, 76 (1988), 159-189.
doi: 10.1016/0022-0396(88)90068-X. |
[9] |
M. Herrero and J. L. Vazquez, Asymptotic behaviour of the solution of a strongly nonlinear parabolic problem, Ann. Fac. Sci. Toulouse (5)ème serie, 3 (1981), 113-127. |
[10] |
S. Kamin and J. L. Vazquez, Fundamental solutions and asymptotic behaviour for the p-Laplacian equation, Rev. Mat. Iberoamericana, 4 (1988), 339-352.
doi: 10.4171/RMI/77. |
[11] |
S. Kamin and J. L. Vazquez, Singular solutions of of some nonlinear parabolic equations, J. Analyse Math., 59 (1992), 51-74.
doi: 10.1007/BF02790217. |
[12] |
J. B. Keller, On solutions of $\Delta u=f(u)$, Comm. Pure Appl. Math., 10 (1957), 503-510. |
[13] |
F. Li, Regularity for entropy solutions of a class of parabolic equations with irregular data, Comment. Math. Univ. Carolin., 48 (2007), 69-82. |
[14] |
M. Marcus and L. Véron, Initial trace of positive solutions to semilinear parabolic inequalities, Adv. Nonlinear Studies, 2 (2002), 395-436. |
[15] |
T. Nguyen Phuoc and L. Véron, Local and global properties of solutions of heat equation with superlinear absorption, Adv. Differential Equations, 16 (2011), 487-522. |
[16] |
S. Segura de Leon and J. Toledo, Regularity for entropy solutions of parabolic p-Laplacian type equations, Publicacions Matemàtiques, 43 (1999), 665-683.
doi: 10.5565/PUBLMAT_43299_08. |
[17] |
J. L. Vazquez, An a priori interior estimate for the solutions of a nonlinear problem representing weak diffusion, Nonlinear Anal., 5 (1981), 95-103.
doi: 10.1016/0362-546X(81)90074-2. |
[18] |
J. L. Vazquez and L. Véron, Isolated singularities of some semilinear elliptic equations, J. Differential Equations, 60 (1985), 301-321.
doi: 10.1016/0022-0396(85)90127-5. |
[19] |
J. L. Vazquez and L. Véron, Different kinds of singular solutions of nonlinear parabolic equations, Nonlinear Problems in Applied Mathematics, 240-249, SIAM, Philadelphia, PA, (1996). |
[20] |
L. Véron, Some remarks on the convergence of approximate solutions of nonlinear evolution equations in Hilbert spaces, Math. Comp., 39 (1982), 325-337.
doi: 10.2307/2007318. |
[21] |
L. Véron, "Singularities of Solutions of Second Other Quasilinear Equations," Pitman Research Notes in Math. Series 353, Adison Wesley, Longman, 1996. |
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