논문KCI 등재
A PARABOLIC SYSTEM WITH NONLOCAL BOUNDARY CONDITIONS AND NONLOCAL SOURCES
대한수학회 (The Korean Mathematical Society)|2012.07|대한수학회논문집 (Communications of the KMS)|제27권 제3호|pp. 629-644
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this work, the authors study the blow-up properties of solutions to a parabolic system with nonlocal boundary conditions and nonlocal sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and precise blow-up rate estimates are also obtained.
Abstract
In this work, the authors study the blow-up properties of solutions to a parabolic system with nonlocal boundary conditions and nonlocal sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and precise blow-up rate estimates are also obtained.
참고문헌 (26)
- J. R. Anderson, "Local existence and uniqueness of solutions of degenerate parabolic equations", Comm. Partial Differential Equations, 16(1), pp.105~143 (1991)
- J. Bebernes, "Total blow-up versus single point blow-up", J. Differential Equations, 73(1), pp.30~44 (1988)
- S. Carl, "Generalized quasilinearization method for reaction- diffusion equations under nonlinear and nonlocal flux conditions", J. Math. Anal. Appl, 271(1), pp.182~205 (2002)
- D. E. Carlson, "Linear thermoelasticity, in Encyclopedia of Physics" (1972), Springer
- Y. J. Chen, "A class of nonlocal and degenerate quasilinear parabolic system not in divergence form", Nonlinear Anal, 71(7-8), pp.3530~3537 (2009)
- Z. J. Cui, "Roles of weight functions to a nonlinear porous medium equation with nonlocal source and nonlocal boundary condition", J. Math. Anal. Appl, 342(1), pp.559~570 (2008)
- W. A. Day, "Extensions of a property of the heat equation to linear thermoelasticity and other theories", Quart. Appl. Math, 40(3), pp.319~330 (1982)
- W. A. Day, "A decreasing property of solutions of parabolic equations with applications to thermoelasticity", Quart. Appl. Math, 40(4), pp.468~475 (1982)
- K. Deng, "Comparison principle for some nonlocal problems", Quart. Appl. Math, 50(3), pp.517~522 (1992)
- W. B. Deng, "Blow-up and global existence for a nonlocal degenerate parabolic system", J. Math. Anal. Appl, 277(1), pp.199~217 (2003)
- L. L. Du, "Blow-up for a degenerate reaction-diffusion system with nonlinear nonlocal sources", J. Comput. Appl. Math, 202(2), pp.237~247 (2007)
- A. Friedman, "Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions", Quart. Appl. Math, 44(3), pp.401~407 (1986)
- A. Friedman, "Blow-up of positive solutions of semilinear heat equations", Indiana Univ. Math. J, 34(2), pp.425~447 (1985)
- L. J. Jiang, "Uniform blow-up profiles and boundary layer for a parabolic system with nonlocal sources", Math. Comput. Modelling, 45(7-8), pp.814~824 (2007)
- Z. G. Lin, "Uniform blowup profile for diffusion equations with nonlocal source and nonlocal boundary", Acta Math. Sci. Ser. B Engl. Ed, 24(3), pp.443~450 (2004)
- C. V. Pao, "Dynamics of reaction-diffusion equations with nonlocal boundary conditions", Quart. Appl. Math, 50(1), pp.173~186 (1995)
- C. V. Pao, "Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions", J. Comput. Appl. Math, 88(1), pp.225~238 (1998)
- C. V. Pao, "Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions", J. Comput. Appl. Math, 136(1-2), pp.227~243 (2001)
- S. Seo, "Blowup of solutions to heat equations with nonlocal boundary conditions", Kobe J. Math, 13(2), pp.123~132 (1996)
- S. Seo, "Global existence and decreasing property of boundary values of solutions to parabolic equations with nonlocal boundary conditions", Pacific J. Math, 193(1), pp.219~226 (2000)
- P. Souplet, "Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source", J. Differential Equations, 153(2), pp.374~406 (1999)
- Y. L. Wang, "Blowup of solutions to a porous medium equation with nonlocal boundary condition", Appl. Math. Comput, 192(2), pp.579~585 (2007)
- Z. Y. Xiang, "Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources", Nonlinear Anal, 61(7), pp.1209~1224 (2005)
- H. M. Yin, "On a class of parabolic equations with nonlocal boundary conditions", J. Math. Anal. Appl, 294(2), pp.712~728 (2004)
- Y. F. Yin, "On nonlinear parabolic equations with nonloal boundary conditions", J. Math. Anal. Appl, 185(1), pp.161~174 (1994)
- S. N. Zheng, "Roles of weight functions in a nonlinear nonlocal parabolic system", Nonlinear Anal, 68(8), pp.2406~2416 (2008)
관련 논문AI추천
Global existence and blow-up for a degenerate reaction-diffusion system with nonlinear localized sources and nonlocal boundary conditionsFei Liang대한수학회 · 대한수학회지2016 · 제53권 제1호Some types of reaction-diffusion systems with nonlocal boundary conditionsWenjie Gao, Yuzhu Han대한수학회 · 대한수학회보2013 · 제50권 제6호Blow-up and global solutions for some parabolic systems under nonlinear boundary conditionsLimin Guo, Lishan Liu, Yonghong Wu, Yu-mei Zou대한수학회 · 대한수학회지2019 · 제56권 제4호CRITICAL EXPONENTS FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUXBotao Chen, Chunlai Mu, Yongsheng Mi대한수학회 · 대한수학회지2011 · 제48권 제3호Local and global existence and blow-up of solutions to a polytropic filtration system with nonlinear memory and nonlinear boundary conditionsJian Wang, Meng-long Su, Zhong Bo Fang대한수학회 · 대한수학회보2013 · 제50권 제1호Blow-up time and blow-up rate for pseudo-parabolic equations with weighted sourceHuafei Di, Yadong Shang대한수학회 · 대한수학회논문집2020 · 제35권 제4호
이 간행물의 다른 논문 (22건)
N-SUBALGEBRAS OF TYPE (∈, ∈ ∨ q) BASED ON POINT N-STRUCTURES IN BCK/BCI-ALGEBRAS전영배, 이경자, Xiaohong Zhangpp. 431-439NOTES ON (σ, τ)-DERIVATIONS OF LIE IDEALS IN PRIME RINGSSeda Oguz, Oznur Golbasipp. 441-448CYCLOTOMIC POLYNOMIALS OVER CYCLOTOMIC FIELDS김성두, 이준복pp. 449-454ON THE RELATIVE ZETA FUNCTION IN FUNCTION FIELDSDaisuke Shiomipp. 455-464FUZZY IDEALS GENERATED BY FUZZY SUBSETS IN SEMIGROUPS전인흥pp. 465-475
