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Multiplicity of solutions of variational systems involving $\phi$-Laplacians with singular $\phi$ and periodic nonlinearities
Asymptotic behavior of singular solutions for a semilinear parabolic equation
1. | Mathematical Institute, Tohoku University, Sendai 980-8578, Japan |
2. | Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551 |
References:
[1] |
L. R. Bragg, The radial heat polynomials and related functions, Trans. Amer. Math. Soc., 119 (1965), 270-290.
doi: 10.1090/S0002-9947-1965-0181769-4. |
[2] |
L. R. Bragg, The radial heat equation and Laplace transforms, SIAM J. Appl. Math., 14 (1966), 986-993.
doi: 10.1137/0114080. |
[3] |
L. R. Bragg, On the solution structure of radial heat problems with singular data, SIAM J. Appl. Math., 15 (1967), 1258-1271.
doi: 10.1137/0115108. |
[4] |
L. R. Bragg, The radial heat equation with pole type data, Bull. Amer. Math. Soc., 73 (1967), 133-135.
doi: 10.1090/S0002-9904-1967-11681-1. |
[5] |
C.-C. Chen and C.-S. Lin, Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations, J. Geometric Analysis, 9 (1999), 221-246. |
[6] |
D. T. Haimo, Functions with the Huygens property, Bull. Amer. Math. Soc., 71 (1965), 528-532.
doi: 10.1090/S0002-9904-1965-11318-0. |
[7] |
D. T. Haimo, Expansions in terms of generalized heat polynomials and their Appell transforms, J. Math. Mech., 15 (1966), 735-758. |
[8] |
O. A. Ladyženskaja, V. A. Solonnikov and N. M. Ural'ceva, "Lineĭnye i Kvazilineĭnye Uravneniya Parabolicheskogo Tipa," (Russian) [Linear and Quasi-linear Equations of Parabolic Type], Izdat. "Nauka," Moscow, 1968, 736 pp. |
[9] |
P. Quittner and Ph. Souplet, "Superlinear Parabolic Problems.Blow-up, Global Existence and Steady States," Birkhäuser Advanced Texts: Basler Lehrbücher, [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 2007. |
[10] |
S. Sato, A singular solution with smooth initial data for a semilinear parabolic equation, Nonlinear Anal., 74 (2011), 1383-1392.
doi: 10.1016/j.na.2010.10.010. |
[11] |
S. Sato and E. Yanagida, Solutions with moving singularities for a semilinear parabolic equation, J. Differential Equations, 246 (2009), 724-748.
doi: 10.1016/j.jde.2008.09.004. |
[12] |
S. Sato and E. Yanagida, Forward self-similar solution with a movingsingularity for a semilinear parabolic equation, Discrete Contin. Dyn. Syst., 26 (2010), 313-331. |
[13] |
S. Sato and E. Yanagida, Singular backward self-similar solutions of a semilinear parabolic equation, Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), 897-906. |
[14] |
S. Sato and E. Yanagida, Appearance of anomalous singularities in a semilinear parabolic equation, Commun. Pure Appl. Anal., 11 (2012), 387-405.
doi: 10.3934/cpaa.2012.11.387. |
[15] |
L. Véron, "Singularities of Solutions of Second Order Quasilinear Equations," Pitman Research Notes in Mathematics Series, 353, Longman, Harlow, 1996. |
show all references
References:
[1] |
L. R. Bragg, The radial heat polynomials and related functions, Trans. Amer. Math. Soc., 119 (1965), 270-290.
doi: 10.1090/S0002-9947-1965-0181769-4. |
[2] |
L. R. Bragg, The radial heat equation and Laplace transforms, SIAM J. Appl. Math., 14 (1966), 986-993.
doi: 10.1137/0114080. |
[3] |
L. R. Bragg, On the solution structure of radial heat problems with singular data, SIAM J. Appl. Math., 15 (1967), 1258-1271.
doi: 10.1137/0115108. |
[4] |
L. R. Bragg, The radial heat equation with pole type data, Bull. Amer. Math. Soc., 73 (1967), 133-135.
doi: 10.1090/S0002-9904-1967-11681-1. |
[5] |
C.-C. Chen and C.-S. Lin, Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations, J. Geometric Analysis, 9 (1999), 221-246. |
[6] |
D. T. Haimo, Functions with the Huygens property, Bull. Amer. Math. Soc., 71 (1965), 528-532.
doi: 10.1090/S0002-9904-1965-11318-0. |
[7] |
D. T. Haimo, Expansions in terms of generalized heat polynomials and their Appell transforms, J. Math. Mech., 15 (1966), 735-758. |
[8] |
O. A. Ladyženskaja, V. A. Solonnikov and N. M. Ural'ceva, "Lineĭnye i Kvazilineĭnye Uravneniya Parabolicheskogo Tipa," (Russian) [Linear and Quasi-linear Equations of Parabolic Type], Izdat. "Nauka," Moscow, 1968, 736 pp. |
[9] |
P. Quittner and Ph. Souplet, "Superlinear Parabolic Problems.Blow-up, Global Existence and Steady States," Birkhäuser Advanced Texts: Basler Lehrbücher, [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 2007. |
[10] |
S. Sato, A singular solution with smooth initial data for a semilinear parabolic equation, Nonlinear Anal., 74 (2011), 1383-1392.
doi: 10.1016/j.na.2010.10.010. |
[11] |
S. Sato and E. Yanagida, Solutions with moving singularities for a semilinear parabolic equation, J. Differential Equations, 246 (2009), 724-748.
doi: 10.1016/j.jde.2008.09.004. |
[12] |
S. Sato and E. Yanagida, Forward self-similar solution with a movingsingularity for a semilinear parabolic equation, Discrete Contin. Dyn. Syst., 26 (2010), 313-331. |
[13] |
S. Sato and E. Yanagida, Singular backward self-similar solutions of a semilinear parabolic equation, Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), 897-906. |
[14] |
S. Sato and E. Yanagida, Appearance of anomalous singularities in a semilinear parabolic equation, Commun. Pure Appl. Anal., 11 (2012), 387-405.
doi: 10.3934/cpaa.2012.11.387. |
[15] |
L. Véron, "Singularities of Solutions of Second Order Quasilinear Equations," Pitman Research Notes in Mathematics Series, 353, Longman, Harlow, 1996. |
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