Large time behavior of solutions to a class of doubly nonlinear parabolic equations
Applications of Mathematics (2008)
- Volume: 53, Issue: 6, page 521-533
- ISSN: 0862-7940
Access Full Article
top
Abstract
topHow to cite
topZhan, Hua Shui. "Large time behavior of solutions to a class of doubly nonlinear parabolic equations." Applications of Mathematics 53.6 (2008): 521-533. <http://eudml.org/doc/37798>.
@article{Zhan2008,
abstract = {We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation $u_t=\mathop \{\{\rm div\}\} (u^\{m-1\}|Du|^\{p-2\}Du)-u^q$ with an initial condition $u(x,0)=u_0(x)$. Here the exponents $m$, $p$ and $q$ satisfy $m+p\ge 3$, $p>1$ and $q>m+p-2$.},
author = {Zhan, Hua Shui},
journal = {Applications of Mathematics},
keywords = {degenerate parabolic equation; large time asymptotic behavior; degenerate parabolic equation; large time asymptotic behavior},
language = {eng},
number = {6},
pages = {521-533},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Large time behavior of solutions to a class of doubly nonlinear parabolic equations},
url = {http://eudml.org/doc/37798},
volume = {53},
year = {2008},
}
TY - JOUR
AU - Zhan, Hua Shui
TI - Large time behavior of solutions to a class of doubly nonlinear parabolic equations
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 6
SP - 521
EP - 533
AB - We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation $u_t=\mathop {{\rm div}} (u^{m-1}|Du|^{p-2}Du)-u^q$ with an initial condition $u(x,0)=u_0(x)$. Here the exponents $m$, $p$ and $q$ satisfy $m+p\ge 3$, $p>1$ and $q>m+p-2$.
LA - eng
KW - degenerate parabolic equation; large time asymptotic behavior; degenerate parabolic equation; large time asymptotic behavior
UR - http://eudml.org/doc/37798
ER -
References
top- Benedetto, E. Di, Degenerate Parabolic Equations, Springer New York (1993). (1993) MR1230384
- Ivanov, A. V. H., 10.1007/BF01671935, J. Sov. Math. 56 (1991), 2320-2347. (1991) Zbl0729.35018MR1031986DOI10.1007/BF01671935
- Kalashnikov, A. S., Some problems of nonlinear parabolic equations of second order, Uspekhi Math. Nauk 42 (1987), 135-176. (1987) MR0898624
- Kamin, S., Vazquez, J. L., 10.4171/RMI/77, Rev. Mat. Iberoam. 4 (1988), 339-354. (1988) MR1028745DOI10.4171/RMI/77
- Ladyzhenskaya, O. A., New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problem for them, Tr. Mat. Inst. Steklova 102 (1967), 95-118. (1967)
- Ladyzhenskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N., 10.1090/mmono/023, American Mathematical Society (AMS) Providence (1968). (1968) DOI10.1090/mmono/023
- Manfredi, J., Vespri, V., Large time behavior of solutions to a class of doubly nonlinear parabolic equations, Electron. J. Differ. Equ. 1994/02 (1994), 1-16. (1994) Zbl0787.35047MR1262933
- Masayoshi, T., 10.1016/0022-247X(88)90053-4, J. Math. Anal. Appl. 132 (1988), 187-212. (1988) MR0942364DOI10.1016/0022-247X(88)90053-4
- Winkler, M., 10.1007/PL00001452, NoDEA, Nonlinear Differ. Equ. Appl. 8 (2001), 343-361. (2001) Zbl0980.35077MR1841613DOI10.1007/PL00001452
- Wu, Z., Zhao, J., Yin, J., Li, H., Nonlinear Diffusion Equations, Word Scientific Singapore (2001). (2001) Zbl0997.35001
- Yang, J., Zhao, J., The asymptotic behavior of solutions of some doubly degenerate nonlinear parabolic equations, Northeast. Math. J. 11 (1995), 241-252. (1995) Zbl0848.35067MR1350918
- Zhao, J., Yuan, H., The Cauchy problem of some nonlinear doubly degenerate parabolic equations, Chin. Ann. Math., Ser. A 16 (1995), 181-196. (1995) Zbl0828.35071MR1341930
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.