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Numerical study of blow-up in the Davey-Stewartson system
Sign-changing solutions of a quasilinear heat equation with a source term
1. | School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China |
2. | Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States |
References:
[1] |
B. Bettioui and A. Gmira, On the radial solutions of a degenerate quasilinear elliptic equation in $R^N$, Ann. Fac. Sci. Toulouse, 8 (1999), 411-438. |
[2] |
M.F. Bidaut-Véron, The $p$-Laplace heat equation with a source term: self-similar solutions revisited, Advanced Nonlinear Studies, 6 (2006), 69-108. |
[3] |
T. Cazenave, F. Dickstein and F.B. Weissler, Sign-changing stationary solutions and blowup for the nonlinear heat equation in a ball Math. Ann., 344 (2009), 431-449.
doi: 10.1007/s00208-008-0312-6. |
[4] |
C. Dohmen and M. Hirose, Structure of positive radial solutions to the Haraux-Weissler equation, Nonlinear Anal., 33 (1998), 51-69.
doi: 10.1016/S0362-546X(97)00542-7. |
[5] |
A. Haraux and F.B. Weissler, Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J., 31 (1982), 167-189.
doi: 10.1512/iumj.1982.31.31016. |
[6] |
L.A. Peletier, D. Terman and F.B. Weissler, On the equation $\Delta u+\frac {1}{2}x \nabla u +f(u)=0$, Arch. Rat. Mech. Anal. 94 (1986), 83-99.
doi: 10.1007/BF00278244. |
[7] |
Y.W. Qi, The existence of moving boundary solution of a porous media equation with a source term, Mathematical Sciences and Applications Gakkōtosho, Tokyo, 6 (1996), 197-215. |
[8] |
Y.W. Qi, The global existence and nonuniqueness of a nonlinear degenerate equation, Nonlinear Anal. 31 (1998), 117-136.
doi: 10.1016/S0362-546X(96)00298-2. |
[9] |
R. Suzuki, Asymptotic behavior of solutions of quasilinear parabolic equations with supercritical nonlinearity, J. Differential Equations, 190 (2003), 150-181.
doi: 10.1016/S0022-0396(02)00086-4. |
[10] |
M. Wang and X. Wang, Existence of positive solutions to a nonlinear initial problem, Nonlinear Anal. 44 (2001), 1133-1136.
doi: 10.1016/S0362-546X(99)00344-2. |
[11] |
F.B. Weissler, Asymptotic analysis of an ordinary differential equation and non-uniqueness for a semilinear partial differential equation, Arch. Rat. Mech. Anal. 91 (1986), 231-245.
doi: 10.1007/BF00250743. |
[12] |
F.B. Weissler, Rapidly decaying solutions of an ordinary differential equation with applications to semilinear elliptic and parabolic partial differential equations, Arch. Rat. Mech. Anal. 91 (1986), 247-266.
doi: 10.1007/BF00250744. |
[13] |
F.B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation Israel J. Math. 38 (1981), 29-40.
doi: 10.1007/BF02761845. |
[14] |
E. Yanagida, Uniqueness of rapidly decreasing solutions to the Haraux-Weissler equation, J. Differential Equations 127 (1996), 561-570.
doi: 10.1006/jdeq.1996.0083. |
show all references
References:
[1] |
B. Bettioui and A. Gmira, On the radial solutions of a degenerate quasilinear elliptic equation in $R^N$, Ann. Fac. Sci. Toulouse, 8 (1999), 411-438. |
[2] |
M.F. Bidaut-Véron, The $p$-Laplace heat equation with a source term: self-similar solutions revisited, Advanced Nonlinear Studies, 6 (2006), 69-108. |
[3] |
T. Cazenave, F. Dickstein and F.B. Weissler, Sign-changing stationary solutions and blowup for the nonlinear heat equation in a ball Math. Ann., 344 (2009), 431-449.
doi: 10.1007/s00208-008-0312-6. |
[4] |
C. Dohmen and M. Hirose, Structure of positive radial solutions to the Haraux-Weissler equation, Nonlinear Anal., 33 (1998), 51-69.
doi: 10.1016/S0362-546X(97)00542-7. |
[5] |
A. Haraux and F.B. Weissler, Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J., 31 (1982), 167-189.
doi: 10.1512/iumj.1982.31.31016. |
[6] |
L.A. Peletier, D. Terman and F.B. Weissler, On the equation $\Delta u+\frac {1}{2}x \nabla u +f(u)=0$, Arch. Rat. Mech. Anal. 94 (1986), 83-99.
doi: 10.1007/BF00278244. |
[7] |
Y.W. Qi, The existence of moving boundary solution of a porous media equation with a source term, Mathematical Sciences and Applications Gakkōtosho, Tokyo, 6 (1996), 197-215. |
[8] |
Y.W. Qi, The global existence and nonuniqueness of a nonlinear degenerate equation, Nonlinear Anal. 31 (1998), 117-136.
doi: 10.1016/S0362-546X(96)00298-2. |
[9] |
R. Suzuki, Asymptotic behavior of solutions of quasilinear parabolic equations with supercritical nonlinearity, J. Differential Equations, 190 (2003), 150-181.
doi: 10.1016/S0022-0396(02)00086-4. |
[10] |
M. Wang and X. Wang, Existence of positive solutions to a nonlinear initial problem, Nonlinear Anal. 44 (2001), 1133-1136.
doi: 10.1016/S0362-546X(99)00344-2. |
[11] |
F.B. Weissler, Asymptotic analysis of an ordinary differential equation and non-uniqueness for a semilinear partial differential equation, Arch. Rat. Mech. Anal. 91 (1986), 231-245.
doi: 10.1007/BF00250743. |
[12] |
F.B. Weissler, Rapidly decaying solutions of an ordinary differential equation with applications to semilinear elliptic and parabolic partial differential equations, Arch. Rat. Mech. Anal. 91 (1986), 247-266.
doi: 10.1007/BF00250744. |
[13] |
F.B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation Israel J. Math. 38 (1981), 29-40.
doi: 10.1007/BF02761845. |
[14] |
E. Yanagida, Uniqueness of rapidly decreasing solutions to the Haraux-Weissler equation, J. Differential Equations 127 (1996), 561-570.
doi: 10.1006/jdeq.1996.0083. |
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