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A PARABOLIC SYSTEM WITH NONLOCAL BOUNDARY CONDITIONS AND NONLOCAL SOURCES
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 Title & Authors
A PARABOLIC SYSTEM WITH NONLOCAL BOUNDARY CONDITIONS AND NONLOCAL SOURCES
Gao, Wenjie; Han, Yuzhu;
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 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.
 Keywords
global existence;blow-up;nonlocal sources;nonlocal boundary conditions;global blow-up;blow-up rate;
 Language
English
 Cited by
 References
1.
J. R. Anderson, Local existence and uniqueness of solutions of degenerate parabolic equations, Comm. Partial Differential Equations 16 (1991), no. 1, 105-143. crossref(new window)

2.
J. Bebernes, A. Bressan, and A. Lacey, Total blow-up versus single point blow-up, J. Differential Equations 73 (1988), no. 1, 30-44. crossref(new window)

3.
S. Carl and V. Lakshmikantham, Generalized quasilinearization method for reaction- diffusion equations under nonlinear and nonlocal flux conditions, J. Math. Anal. Appl. 271 (2002), no. 1, 182-205. crossref(new window)

4.
D. E. Carlson, Linear thermoelasticity, in Encyclopedia of Physics, Springer, Berlin, 1972.

5.
Y. J. Chen and M. X. Wang, A class of nonlocal and degenerate quasilinear parabolic system not in divergence form, Nonlinear Anal. 71 (2009), no. 7-8, 3530-3537. crossref(new window)

6.
Z. J. Cui and Z. D. Yang, Roles of weight functions to a nonlinear porous medium equation with nonlocal source and nonlocal boundary condition, J. Math. Anal. Appl. 342 (2008), no. 1, 559-570. crossref(new window)

7.
W. A. Day, Extensions of a property of the heat equation to linear thermoelasticity and other theories, Quart. Appl. Math. 40 (1982/83), no. 3, 319-330.

8.
W. A. Day, A decreasing property of solutions of parabolic equations with applications to thermoelasticity, Quart. Appl. Math. 40 (1982/83), no. 4, 468-475.

9.
K. Deng, Comparison principle for some nonlocal problems, Quart. Appl. Math. 50 (1992), no. 3, 517-522.

10.
W. B. Deng, Y. X. Li, and C. H. Xie, Blow-up and global existence for a nonlocal degenerate parabolic system, J. Math. Anal. Appl. 277 (2003), no. 1, 199-217. crossref(new window)

11.
L. L. Du, Blow-up for a degenerate reaction-diffusion system with nonlinear nonlocal sources, J. Comput. Appl. Math. 202 (2007), no. 2, 237-247. crossref(new window)

12.
A. Friedman, Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions, Quart. Appl. Math. 44 (1986), no. 3, 401-407.

13.
A. Friedman and J. B. Mcleod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), no. 2, 425-447. crossref(new window)

14.
L. J. Jiang and H. L. Li, Uniform blow-up profiles and boundary layer for a parabolic system with nonlocal sources, Math. Comput. Modelling 45 (2007), no. 7-8, 814-824. crossref(new window)

15.
Z. G. Lin and Y. R. Lin, Uniform blowup profile for diffusion equations with nonlocal source and nonlocal boundary, Acta Math. Sci. Ser. B Engl. Ed. 24 (2004), no. 3, 443-450.

16.
C. V. Pao, Dynamics of reaction-diffusion equations with nonlocal boundary conditions, Quart. Appl. Math. 50 (1995), no. 1, 173-186.

17.
C. V. Pao, Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions, J. Comput. Appl. Math. 88 (1998), no. 1, 225-238. crossref(new window)

18.
C. V. Pao, Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions, J. Comput. Appl. Math. 136 (2001), no. 1-2, 227-243. crossref(new window)

19.
S. Seo, Blowup of solutions to heat equations with nonlocal boundary conditions, Kobe J. Math. 13 (1996), no. 2, 123-132.

20.
S. Seo, Global existence and decreasing property of boundary values of solutions to parabolic equations with nonlocal boundary conditions, Pacific J. Math. 193 (2000), no. 1, 219-226. crossref(new window)

21.
P. Souplet, Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source, J. Differential Equations 153 (1999), no. 2, 374-406. crossref(new window)

22.
Y. L. Wang, C. L. Mu, and Z. Y. Xiang, Blowup of solutions to a porous medium equation with nonlocal boundary condition, Appl. Math. Comput. 192 (2007), no. 2, 579-585. crossref(new window)

23.
Z. Y. Xiang, X. G. Hu, and C. L. Mu, Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources, Nonlinear Anal. 61 (2005), no. 7, 1209-1224. crossref(new window)

24.
H. M. Yin, On a class of parabolic equations with nonlocal boundary conditions, J. Math. Anal. Appl. 294 (2004), no. 2, 712-728. crossref(new window)

25.
Y. F. Yin, On nonlinear parabolic equations with nonloal boundary conditions, J. Math. Anal. Appl. 185 (1994), no. 1, 161-174. crossref(new window)

26.
S. N. Zheng and L. H. Kong, Roles of weight functions in a nonlinear nonlocal parabolic system, Nonlinear Anal. 68 (2008), no. 8, 2406-2416. crossref(new window)