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A PARABOLIC SYSTEM WITH NONLOCAL BOUNDARY CONDITIONS AND NONLOCAL SOURCES

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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)

  1. J. R. Anderson, "Local existence and uniqueness of solutions of degenerate parabolic equations", Comm. Partial Differential Equations, 16(1), pp.105~143 (1991)
  2. J. Bebernes, "Total blow-up versus single point blow-up", J. Differential Equations, 73(1), pp.30~44 (1988)
  3. 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)
  4. D. E. Carlson, "Linear thermoelasticity, in Encyclopedia of Physics" (1972), Springer
  5. 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)
  6. 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)
  7. 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)
  8. W. A. Day, "A decreasing property of solutions of parabolic equations with applications to thermoelasticity", Quart. Appl. Math, 40(4), pp.468~475 (1982)
  9. K. Deng, "Comparison principle for some nonlocal problems", Quart. Appl. Math, 50(3), pp.517~522 (1992)
  10. W. B. Deng, "Blow-up and global existence for a nonlocal degenerate parabolic system", J. Math. Anal. Appl, 277(1), pp.199~217 (2003)
  11. 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)
  12. A. Friedman, "Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions", Quart. Appl. Math, 44(3), pp.401~407 (1986)
  13. A. Friedman, "Blow-up of positive solutions of semilinear heat equations", Indiana Univ. Math. J, 34(2), pp.425~447 (1985)
  14. 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)
  15. 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)
  16. C. V. Pao, "Dynamics of reaction-diffusion equations with nonlocal boundary conditions", Quart. Appl. Math, 50(1), pp.173~186 (1995)
  17. 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)
  18. C. V. Pao, "Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions", J. Comput. Appl. Math, 136(1-2), pp.227~243 (2001)
  19. S. Seo, "Blowup of solutions to heat equations with nonlocal boundary conditions", Kobe J. Math, 13(2), pp.123~132 (1996)
  20. 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)
  21. 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)
  22. Y. L. Wang, "Blowup of solutions to a porous medium equation with nonlocal boundary condition", Appl. Math. Comput, 192(2), pp.579~585 (2007)
  23. Z. Y. Xiang, "Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources", Nonlinear Anal, 61(7), pp.1209~1224 (2005)
  24. H. M. Yin, "On a class of parabolic equations with nonlocal boundary conditions", J. Math. Anal. Appl, 294(2), pp.712~728 (2004)
  25. Y. F. Yin, "On nonlinear parabolic equations with nonloal boundary conditions", J. Math. Anal. Appl, 185(1), pp.161~174 (1994)
  26. S. N. Zheng, "Roles of weight functions in a nonlinear nonlocal parabolic system", Nonlinear Anal, 68(8), pp.2406~2416 (2008)

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