ANALYSIS FOR TIME DISCRETE APPROXIMATIONS OF BLOW-UP SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

被引：15

作者：

Kyza, Irene ^{[1
]}

Makridakis, Charalambos ^{[2
,3
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ Crete, Dept Appl Math, Iraklion 71409, Greece

[3] FORTH, Inst Appl & Computat Math, Iraklion 71110, Greece

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 01期

关键词：

semilinear parabolic equations; blow-up solutions and rate; conditional a posteriori estimates; backward Euler method; Crank-Nicolson method; reconstruction technique; energy techniques; fixed point arguments; Duhamel's principle; POSTERIORI ERROR ANALYSIS; CRANK-NICOLSON METHOD; BEHAVIOR;

D O I：

10.1137/100796819

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank-Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time.

引用

页码：405 / 426

页数：22

共 50 条

[11] Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory
Souplet, P
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2004, 55 (01): : 28 - 31
[12] Blow-up and nonexistence of solutions of some semilinear degenerate parabolic equations
Wu, Hui
BOUNDARY VALUE PROBLEMS, 2015,
[13] On the blow-up of sign-changing solutions to semilinear parabolic equations
S. I. Pohozaev
Doklady Mathematics, 2010, 81 : 185 - 187
[14] A condition for blow-up solutions to discrete semilinear wave equations on networks
Choi, Min-Jun
APPLICABLE ANALYSIS, 2022, 101 (06) : 2008 - 2018
[15] BLOW-UP FOR SEMILINEAR PARABOLIC EQUATIONS WITH A GRADIENT TERM
QUITTNER, P
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1991, 14 (06) : 413 - 417
[16] Complete blow-up for degenerate semilinear parabolic equations
Chan, CY
Yang, J
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 113 (1-2) : 353 - 364
[17] Blow-up for semilinear parabolic equations with nonlinear memory
Yuxiang Li
Chunhong Xie
Zeitschrift für angewandte Mathematik und Physik ZAMP, 2004, 55 : 15 - 27
[18] BLOW-UP AT THE BOUNDARY FOR DEGENERATE SEMILINEAR PARABOLIC EQUATIONS
FLOATER, MS
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1991, 114 (01) : 57 - 77
[19] Blow-up in semilinear parabolic equations with weak diffusion
Short, M
Kapila, AK
COMBUSTION THEORY AND MODELLING, 1998, 2 (03) : 283 - 291
[20] Note on a question of blow-up for semilinear parabolic equations
Wang, Mingxin
Zhang, Qin
Journal of Mathematical Analysis and Applications, 1996, 198 (01):

← 1 2 3 4 5 →