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Blowup at space infinity of a solution with a moving singularity for a semilinear parabolic equation
1.  Mathematical Institute, Tohoku University, Sendai 9808578 
References:
[1] 
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), 221246. 
[2] 
H. Fujita, On the blowing up of solutions of the Cauchy problem for $u_t=\Delta u+u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 16 (1966), 105113. 
[3] 
Y. Giga and N. Umeda, Blowup directions at space infinity for solutions of semilinear heat equations, Bol. Soc. Parana. Mat., 23 (2005), 928. doi: 10.5269/bspm.v23i12.7450. 
[4] 
Y. Giga and N. Umeda, On blowup at space infinity for semilinear heat equations, J. Math. Anal. Appl., 316 (2006), 538555. doi: 10.1016/j.jmaa.2005.05.007. 
[5] 
A. A. Lacey, The form of blowup for nonlinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 98 (1984), 183202. 
[6] 
O. A. Ladyž zenskaja, V. A. Solonnikov and N. M. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc., Trans. Math. Monographs 23, Providence, 1968. 
[7] 
N. Mizoguchi and E. Yanagida, Life span of solutions for a semilinear parabolic problem with small diffusion, J. Math. Anal. Appl., 261 (2001), 350368. doi: 10.1006/jmaa.2001.7530. 
[8] 
P. Quittner and Ph. Souplet, "Superlinear Parabolic Problems. Blowup, Global Existence and Steady States," Birkhäuser Advanced Texts, Birkhäuser, Basel, 2007. 
[9] 
S. Sato and E. Yanagida, Solutions with Moving Singularities for a Semilinear Parabolic Equation, J. Differential Equations, 246 (2009), 724748. doi: 10.1016/j.jde.2008.09.004. 
[10] 
S. Sato and E. Yanagida, Forward selfsimilar solution with a moving singularity for a semilinear parabolic equation, Discrete and Continuous Dynamical SystemsSeries A, 26 (2010), 313331. doi: 10.3934/dcds.2010.26.313. 
[11] 
S. Sato and E. Yanagida, Appearance of anomalous singularities in a semilinear parabolic equation,, preprint., (). 
[12] 
Y. Seki, On directional blowup for quasilinear parabolic equations with fast diffusion, J. Math. Anal. Appl., 338 (2008), 572587. doi: 10.1016/j.jmaa.2007.05.033. 
[13] 
Y. Seki, R. Suzuki and N. Umeda, Blowup directions for quasilinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 379405. doi: 10.1017/S0308210506000801. 
[14] 
M. Shimojō, The global profile of blowup at space infinity in semilinear heat equations, J. Math. Kyoto Univ., 48 (2008), 339361. 
[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] 
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), 221246. 
[2] 
H. Fujita, On the blowing up of solutions of the Cauchy problem for $u_t=\Delta u+u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 16 (1966), 105113. 
[3] 
Y. Giga and N. Umeda, Blowup directions at space infinity for solutions of semilinear heat equations, Bol. Soc. Parana. Mat., 23 (2005), 928. doi: 10.5269/bspm.v23i12.7450. 
[4] 
Y. Giga and N. Umeda, On blowup at space infinity for semilinear heat equations, J. Math. Anal. Appl., 316 (2006), 538555. doi: 10.1016/j.jmaa.2005.05.007. 
[5] 
A. A. Lacey, The form of blowup for nonlinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 98 (1984), 183202. 
[6] 
O. A. Ladyž zenskaja, V. A. Solonnikov and N. M. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc., Trans. Math. Monographs 23, Providence, 1968. 
[7] 
N. Mizoguchi and E. Yanagida, Life span of solutions for a semilinear parabolic problem with small diffusion, J. Math. Anal. Appl., 261 (2001), 350368. doi: 10.1006/jmaa.2001.7530. 
[8] 
P. Quittner and Ph. Souplet, "Superlinear Parabolic Problems. Blowup, Global Existence and Steady States," Birkhäuser Advanced Texts, Birkhäuser, Basel, 2007. 
[9] 
S. Sato and E. Yanagida, Solutions with Moving Singularities for a Semilinear Parabolic Equation, J. Differential Equations, 246 (2009), 724748. doi: 10.1016/j.jde.2008.09.004. 
[10] 
S. Sato and E. Yanagida, Forward selfsimilar solution with a moving singularity for a semilinear parabolic equation, Discrete and Continuous Dynamical SystemsSeries A, 26 (2010), 313331. doi: 10.3934/dcds.2010.26.313. 
[11] 
S. Sato and E. Yanagida, Appearance of anomalous singularities in a semilinear parabolic equation,, preprint., (). 
[12] 
Y. Seki, On directional blowup for quasilinear parabolic equations with fast diffusion, J. Math. Anal. Appl., 338 (2008), 572587. doi: 10.1016/j.jmaa.2007.05.033. 
[13] 
Y. Seki, R. Suzuki and N. Umeda, Blowup directions for quasilinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 379405. doi: 10.1017/S0308210506000801. 
[14] 
M. Shimojō, The global profile of blowup at space infinity in semilinear heat equations, J. Math. Kyoto Univ., 48 (2008), 339361. 
[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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