On the interior derivative blow-up for the curvature evolution of capillary surfaces
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- by Keisui Asai and Naoyuki Ishimura
- Proc. Amer. Math. Soc. 126 (1998), 835-840
- DOI: https://doi.org/10.1090/S0002-9939-98-04084-2
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Abstract:
We give examples of the interior derivative blow-up solutions for the curvature evolution of capillary surfaces over a bounded domain in $\mathbf {R}^{N}$.References
- C. V. Pao, Quasisolutions and global attractor of reaction-diffusion systems, Nonlinear Anal. 26 (1996), no. 12, 1889–1903. MR 1386121, DOI 10.1016/0362-546X(95)00058-4
- K.Asai, Interior derivative blow-up for the curvature evolution of capillary surfaces, Thesis, University of Tokyo (1996).
- Tomasz Dłotko, Examples of parabolic problems with blowing-up derivatives, J. Math. Anal. Appl. 154 (1991), no. 1, 226–237. MR 1087970, DOI 10.1016/0022-247X(91)90082-B
- Marek Fila and Gary M. Lieberman, Derivative blow-up and beyond for quasilinear parabolic equations, Differential Integral Equations 7 (1994), no. 3-4, 811–821. MR 1270105
- Robert Finn, Equilibrium capillary surfaces, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 284, Springer-Verlag, New York, 1986. MR 816345, DOI 10.1007/978-1-4613-8584-4
- Yoshikazu Giga, Interior derivative blow-up for quasilinear parabolic equations, Discrete Contin. Dynam. Systems 1 (1995), no. 3, 449–461. MR 1355884, DOI 10.3934/dcds.1995.1.449
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190, DOI 10.1007/978-3-642-61798-0
- Naoyuki Ishimura, Existence of symmetric capillary surfaces via curvature evolution, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40 (1993), no. 2, 419–427. MR 1255049
- N.Kutev, Global solvability and boundary gradient blow up for one dimensional parabolic equations, in “Progress in Partial Differential Equations : Elliptic and Parabolic Problems," Eds. C.Bandle, J.Bemelmans, M.Chipot and M.Grüter, Longman, 1992, pp. 176-181.
- N. Kutev, Gradient blow-ups and global solvability after the blow-up time for nonlinear parabolic equations, Evolution equations, control theory, and biomathematics (Han sur Lesse, 1991) Lecture Notes in Pure and Appl. Math., vol. 155, Dekker, New York, 1994, pp. 301–306. MR 1254908
- J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 413–496. MR 282058, DOI 10.1098/rsta.1969.0033
- Andrew Stone, Evolutionary existence proofs for the pendant drop and $n$-dimensional catenary problems, Pacific J. Math. 164 (1994), no. 1, 147–178. MR 1267505, DOI 10.2140/pjm.1994.164.147
Bibliographic Information
- Keisui Asai
- Affiliation: System Laboratory, Fujitsu Cooperation, Mihama, Chiba 261, Japan
- Email: keisui@tokyo.se.fujitsu.co.jp
- Naoyuki Ishimura
- Affiliation: Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186, Japan
- Email: ishimura@math.hit-u.ac.jp
- Received by editor(s): March 28, 1996
- Received by editor(s) in revised form: September 10, 1996
- Communicated by: Jeffrey B. Rauch
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 835-840
- MSC (1991): Primary 35B40, 35K55, 58G11
- DOI: https://doi.org/10.1090/S0002-9939-98-04084-2
- MathSciNet review: 1422841