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Periodically growing solutions in a class of strongly monotone semiflows
Selfsimilar solutions in a sector for a quasilinear parabolic equation
1.  Department of Mathematics, Tongji University, Shanghai 200092 
References:
[1] 
P. Brunovský, P. Poláčik and B. Sandstede, Convergence in general periodic parabolic equation in one space dimension,, Nonlinear Anal., 18 (1992), 209. doi: 10.1016/0362546X(92)90059N. 
[2] 
Y.L. Chang, J.S. Guo and Y. Kohsaka, On a twopoint free boundary problem for a quasilinear parabolic equation,, Asymptotic Anal., 34 (2003), 333. 
[3] 
X. Chen and J.S. Guo, Motion by curvature of planar curves with end points moving freely on a line,, Math. Ann., 350 (2011), 277. doi: 10.1007/s0020801005587. 
[4] 
H.H. Chern, J.S. Guo and C.P. Lo, The selfsimilar expanding curve for the curvature flow equation,, Proc. Amer. Math. Soc., 131 (2003), 3191. doi: 10.1090/S0002993903070552. 
[5] 
G. Dong, Initial and nonlinear oblique boundary value problems for fully nonlinear parabolic equations,, J. Partial Differential Equations, 1 (1988), 12. 
[6] 
A. Friedman, "Partial Differential Equations of Parabolic Type,", PrenticeHall, (1964). 
[7] 
M.H. Giga, Y. Giga and H. Hontani, Selfsimilar expanding solutions in a sector for a crystalline flow,, SIAM J. Math. Anal., 37 (2005), 1207. doi: 10.1137/040614372. 
[8] 
J.S. Guo and B. Hu, A shrinking twopoint free boundary problem for a quasilinear parabolic equation,, Quart. Appl. Math., 64 (2006), 413. 
[9] 
J.S. Guo and Y. Kohsaka, Selfsimilar solutions of twopoint free boundary problem for heat equation,, in, (2002), 94. 
[10] 
D. Hilhorst, R. van der Hout, M. Mimura and I. Ohnishi, A mathematical study of the onedimensional Keller and Rubinow model for Liesegang bands,, J. Stat. Phys., 135 (2009), 107. doi: 10.1007/s1095500997019. 
[11] 
J. B. Keller and S. I. Rubinow, Recurrent precipitation and Liesegang rings,, J. Chem. Phys., 74 (1981), 5000. doi: 10.1063/1.441752. 
[12] 
Y. Kohsaka, Free boundary problem for quasilinear parabolic equation with fixed angle of contact to a boundary,, Nonlinear Anal., 45 (2001), 865. doi: 10.1016/S0362546X(99)004228. 
[13] 
G. M. Lieberman, "Second Order Parabolic Differential Equations,", World Scientific Publishing Co., (1996). 
[14] 
O. A. Ladyzhenskia, V. A. Solonnikov and N. N. Uraltseva, "Linear and Quasilinear Equations of Parabolic Type,", Amer. Math. Soc., (1968). 
[15] 
B. Lou, H. Matano and K. I. Nakamura, Recurrent traveling waves in a twodimensional sawtoothed cylinder and their average speed,, preprint., (). 
[16] 
H. Matano, K. I. Nakamura and B. Lou, Periodic traveling waves in a twodimensional cylinder with sawtoothed boundary and their homogenization limit,, Netw. Heterog. Media, 1 (2006), 537. doi: 10.3934/nhm.2006.1.537. 
[17] 
D. A. V. Stow, "Sedimentary Rocks in the Field: A Color Guide,", Academic Press, (2005). 
[18] 
K. H. W. J. Ten Tusscher and A. V. Panfilov, Wave propagation in excitable media with randomly distributed obstacles,, Multiscale Model. Simul., 3 (2005), 265. doi: 10.1137/030602654. 
show all references
References:
[1] 
P. Brunovský, P. Poláčik and B. Sandstede, Convergence in general periodic parabolic equation in one space dimension,, Nonlinear Anal., 18 (1992), 209. doi: 10.1016/0362546X(92)90059N. 
[2] 
Y.L. Chang, J.S. Guo and Y. Kohsaka, On a twopoint free boundary problem for a quasilinear parabolic equation,, Asymptotic Anal., 34 (2003), 333. 
[3] 
X. Chen and J.S. Guo, Motion by curvature of planar curves with end points moving freely on a line,, Math. Ann., 350 (2011), 277. doi: 10.1007/s0020801005587. 
[4] 
H.H. Chern, J.S. Guo and C.P. Lo, The selfsimilar expanding curve for the curvature flow equation,, Proc. Amer. Math. Soc., 131 (2003), 3191. doi: 10.1090/S0002993903070552. 
[5] 
G. Dong, Initial and nonlinear oblique boundary value problems for fully nonlinear parabolic equations,, J. Partial Differential Equations, 1 (1988), 12. 
[6] 
A. Friedman, "Partial Differential Equations of Parabolic Type,", PrenticeHall, (1964). 
[7] 
M.H. Giga, Y. Giga and H. Hontani, Selfsimilar expanding solutions in a sector for a crystalline flow,, SIAM J. Math. Anal., 37 (2005), 1207. doi: 10.1137/040614372. 
[8] 
J.S. Guo and B. Hu, A shrinking twopoint free boundary problem for a quasilinear parabolic equation,, Quart. Appl. Math., 64 (2006), 413. 
[9] 
J.S. Guo and Y. Kohsaka, Selfsimilar solutions of twopoint free boundary problem for heat equation,, in, (2002), 94. 
[10] 
D. Hilhorst, R. van der Hout, M. Mimura and I. Ohnishi, A mathematical study of the onedimensional Keller and Rubinow model for Liesegang bands,, J. Stat. Phys., 135 (2009), 107. doi: 10.1007/s1095500997019. 
[11] 
J. B. Keller and S. I. Rubinow, Recurrent precipitation and Liesegang rings,, J. Chem. Phys., 74 (1981), 5000. doi: 10.1063/1.441752. 
[12] 
Y. Kohsaka, Free boundary problem for quasilinear parabolic equation with fixed angle of contact to a boundary,, Nonlinear Anal., 45 (2001), 865. doi: 10.1016/S0362546X(99)004228. 
[13] 
G. M. Lieberman, "Second Order Parabolic Differential Equations,", World Scientific Publishing Co., (1996). 
[14] 
O. A. Ladyzhenskia, V. A. Solonnikov and N. N. Uraltseva, "Linear and Quasilinear Equations of Parabolic Type,", Amer. Math. Soc., (1968). 
[15] 
B. Lou, H. Matano and K. I. Nakamura, Recurrent traveling waves in a twodimensional sawtoothed cylinder and their average speed,, preprint., (). 
[16] 
H. Matano, K. I. Nakamura and B. Lou, Periodic traveling waves in a twodimensional cylinder with sawtoothed boundary and their homogenization limit,, Netw. Heterog. Media, 1 (2006), 537. doi: 10.3934/nhm.2006.1.537. 
[17] 
D. A. V. Stow, "Sedimentary Rocks in the Field: A Color Guide,", Academic Press, (2005). 
[18] 
K. H. W. J. Ten Tusscher and A. V. Panfilov, Wave propagation in excitable media with randomly distributed obstacles,, Multiscale Model. Simul., 3 (2005), 265. doi: 10.1137/030602654. 
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