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Some types of reaction-diffusion systems with nonlocal boundary conditions

Wenjie Gao|Yuzhu Han
대한수학회 (The Korean Mathematical Society)|2013.11|대한수학회보 (Bulletin of the KMS)|제50권 제6호|pp. 1765-1780

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참고문헌

키워드

nonlocal boundary conditionnonlocal sourceblow-up ratelocalized sourceblow-up profile
주제분류수학

초록

This paper deals with some types of semilinear parabolic systems with localized or nonlocal sources and nonlocal boundary conditions. The authors first derive some global existence and blow-up criteria. And then, for blow-up solutions, they study the global blow-up property as well as the precise blow-up rate estimates, which has been seldom studied until now.

Abstract

This paper deals with some types of semilinear parabolic systems with localized or nonlocal sources and nonlocal boundary conditions. The authors first derive some global existence and blow-up criteria. And then, for blow-up solutions, they study the global blow-up property as well as the precise blow-up rate estimates, which has been seldom studied until now.

참고문헌 (32)

  1. J. R. Anderson, "Global existence for degenerate parabolic equations with a non-local forcing", Math. Methods Appl. Sci, 20(13), pp.1069~1087 (1997)
  2. J. Bebernes, "Mathematical Problems from Combustion Theory" (1989), Springer- Verlag
  3. K. Bimpong-Bota, "J. Ross, Far-from-equilibrium phenomena at local cites of reaction", J. Chem. Phys, 60, pp.3124~3133 (1974)
  4. D. E. Carlson, "Linear thermoelasticity, Encyclopedia" (1972), Springer
  5. J. M. Chadam, "The blowup property of solutions to some diffusion equations with localized nonlinear reactions", J. Math. Anal. Appl, 169(2), pp.313~328 (1992)
  6. Y. Chen, "Asymptotic blow-up behavior for a nonlocal degenerate parabolic equation", J. Math. Anal. Appl, 330(2), pp.852~863 (2007)
  7. A. Friedman, "Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions", Quart. Appl. Math, 44(3), pp.401~407 (1986)
  8. A. Friedman, "Blow-up of positive solutions of semilinear heat equa- tions", Indiana Univ. Math. J, 34(2), pp.425~447 (1985)
  9. 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)
  10. W. A. Day, "A decreasing property of solutions of parabolic equations with applications to thermoelasticity", Quart. Appl. Math, 40(4), pp.468~475 (1983)
  11. K. Deng, "Comparison principle for some nonlocal problems", Quart. Appl. Math, 50(3), pp.517~522 (1992)
  12. K. Deng, "The role of critical exponents in blow-up theorems: the sequel", J. Math. Anal. Appl, 243(1), pp.85~126 (2000)
  13. Y. Han, "Global existence and blow-up for a class of degenerate parabolic systems with localized source", Acta Appl. Math, 112(2), pp.251~261 (2010)
  14. L. H. Kong, "Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries", Sci. China Ser. A, 50(9), pp.1251~1266 (2007)
  15. H. A. Levine, "The role of critical exponents in blow up theorems", SIAM Rev, 32, pp.262~288 (1990)
  16. H. L. Li, "Properties of blow-up solutions to a parabolic system with nonlinear localized terms", Discrete Contin. Dyn. Syst, 13(3), pp.683~700 (2005)
  17. P. Ortoleva, "Local structures in chemical reactions with heterogeneous catal- ysis", J. Chem. Phys, 56, pp.4397~4400 (1972)
  18. C. V. Pao, "Nonlinear Parabolic and Elliptic Equations" (1992), Plenum
  19. C. V. Pao, "Dynamics of reaction-diffusion equations with nonlocal boundary conditions", Quart. Appl. Math, 50(1), pp.173~186 (1995)
  20. 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)
  21. C. V. Pao, "Numerical solutions of reaction-diffusion equations with nonlocal boundary con- ditions", J. Comput. Appl. Math, 136(1), pp.227~243 (2001)
  22. S. Seo, "Blowup of solutions to heat equations with nonlocal boundary conditions", Kobe J. Math, 13(2), pp.123~132 (1996)
  23. 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)
  24. P. Souplet, "Blow up in nonlocal reaction-diffusion equations", SIAM J. Math. Anal, 29(6), pp.1301~1334 (1998)
  25. 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)
  26. Y. L. Wang, "Blowup of solutions to a porous medium equation with nonlocal boundary condition", Appl. Math. Comput, 192(2), pp.579~585 (2007)
  27. M. X. Wang, "Properties of positive solutions for non-local reaction- diffusion problems", Math. Methods Appl. Sci, 19(14), pp.1141~1156 (1996)
  28. Y. L. Wang, "Blowup analysis for a semilinear parabolic system with nonlocal boundary condition", Boundary Value Problems (2009)
  29. Z. Y. Xiang, "Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources", Nonlinear Anal, 61(7), pp.1209~1224 (2005)
  30. H. M. Yin, "On a class of parabolic equations with nonlocal boundary conditions", J. Math. Anal. Appl, 294(2), pp.712~728 (2004)
  31. Y. F. Yin, "On nonlinear parabolic equations with nonloal boundary conditions", J. Math. Anal. Appl, 185(1), pp.161~174 (1994)
  32. 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 제1호A PARABOLIC SYSTEM WITH NONLOCAL BOUNDARY CONDITIONS AND NONLOCAL SOURCESWenjie Gao, Yuzhu Han대한수학회 · 대한수학회논문집2012 · 제27권 제3호Blow-up and global solutions for some parabolic systems under nonlinear boundary conditionsLimin Guo, Lishan Liu, Yonghong Wu, Yu-mei Zou대한수학회 · 대한수학회지2019 · 제56권 제4호PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL REACTION-DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITIONChunlai Mu, Dengming Liu, Shouming Zhou대한수학회 · 대한수학회지2010 · 제47권 제6호Blow-up rate estimates for a system of reaction-diffusion equations with absorptionChunlai Mu, Qiong Chen, Zhaoyin Xiang대한수학회 · 대한수학회지2007 · 제44권 제4호CRITICAL EXPONENTS FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUXBotao Chen, Chunlai Mu, Yongsheng Mi대한수학회 · 대한수학회지2011 · 제48권 제3호

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