| [1] |
M. J. Álvarez, A. Ferragut and X. Jarque,
A survey on the blow up technique, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 21 (2011), 3103-3118.
doi: 10.1142/S0218127411030416.
|
| [2] |
K. Anada, I. Fukuda and M. Tsutsumi,
Regional blow-up and decay of solutions to the initial-boundary value problem for $u_{t} = uu_xx-\gamma (u_{x})^{2}+ku^{2}$, Funkcial. Ekvac., 39 (1996), 367-387.
|
| [3] |
K. Anada and T. Ishiwata,
Asymptotic behavior of blow-up solutions to a degenerate parabolic equation, J. Math-for-Ind., 2011 (2011), 1-8.
|
| [4] |
K. Anada and T. Ishiwata,
Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation, J. Differential Equations, 262 (2017), 181-271.
doi: 10.1016/j.jde.2016.09.023.
|
| [5] |
S. B. Angenent and J. J. L. Velázquez,
Asymptotic shape of cusp singularities in curve shortening, Duke Math. J., 77 (1995), 71-110.
doi: 10.1215/S0012-7094-95-07704-7.
|
| [6] |
M. Brunella and M. Miari,
Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra, J. Differential Equations, 85 (1990), 338-366.
doi: 10.1016/0022-0396(90)90120-E.
|
| [7] |
J. Carr, Applications of Centre Manifold Theory, Springer-Verlag, New York, 1981.
|
| [8] |
F. Dumortier, J. Llibre and J. C. Artés, Qualitative Theory of Planar Differential Systems, Springer-Verlag, Berlin Heidelberg, 2006.
|
| [9] |
M. Gage and R. S. Hamilton,
The heat equation shrinking convex plane curves, J. Differential Geom., 23 (1986), 69-96.
|
| [10] |
M. A. Grayson,
The heat equation shrinks embedded plane curves to round points, J. Differential Geom., 26 (1987), 285-314.
|
| [11] |
Y. Ichida, Traveling waves with singularities in a damped hyperbolic MEMS type equation in the presence of negative powers nonlinearity, submitted.
|
| [12] |
Y. Ichida, K. Matsue and T. O. Sakamoto,
A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations, JSIAM Lett., 12 (2020), 65-68.
doi: 10.14495/jsiaml.12.65.
|
| [13] |
Y. Ichida and T. O. Sakamoto,
Quasi traveling waves with quenching in a reaction-diffusion equation in the presence of negative powers nonlinearity, Proc. Japan Acad. Ser. A Math. Sci., 96 (2020), 1-6.
doi: 10.3792/pjaa.96.001.
|
| [14] |
Y. Ichida and T. O. Sakamoto,
Radial symmetric stationary solutions for a MEMS type reaction-diffusion equation with spatially dependent nonlinearity, Jpn. J. Ind. Appl. Math., 38 (2021), 297-322.
doi: 10.1007/s13160-020-00438-8.
|
| [15] |
Y. Ichida and T. O. Sakamoto,
Traveling wave solutions for degenerate nonlinear parabolic equations, J. Elliptic Parabol. Equ., 6 (2020), 795-832.
doi: 10.1007/s41808-020-00080-y.
|
| [16] |
Y. Ichida and T. O. Sakamoto, Singular stationary solutions for a MEMS type reaction-diffusion equation with fringing field, submitted.
|
| [17] |
C. Kuehn, Multiple Time Scale Dynamics, Springer International Publishing, 2015.
doi: 10.1007/978-3-319-12316-5.
|
| [18] |
B. C. Low,
Resitive diffusion of force-fee magnetic fields in a passive medium, Astrophys. J., 181 (1973), 209-226.
|
| [19] |
B. C. Low,
Nonlinear classical diffusion in a contained plasma, Phys. Fluids, 25 (1982), 402-407.
doi: 10.1063/1.863749.
|
| [20] |
K. Matsue,
On blow-up solutions of differential equations with Poincaré type compactificaions, SIAM J. Appl. Dyn. Syst., 17 (2018), 2249-2288.
doi: 10.1137/17M1124498.
|
| [21] |
K. Matsue,
Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs, J. Differential Equations, 267 (2019), 7313-7368.
doi: 10.1016/j.jde.2019.07.022.
|
| [22] |
C.-C. Poon,
Blow-up of a degenerate non-linear heat equation, Taiwanese J. Math., 15 (2011), 1201-1225.
doi: 10.11650/twjm/1500406295.
|
| [23] |
C.-C. Poon,
Blowup rate of solutions of a degenerate nonlinear parabolic equation, Discrete Contin. Dyn. System. Ser. B, 24 (2019), 5317-5336.
doi: 10.3934/dcdsb.2019060.
|
