본문 바로가기
KERD
논문KCI 등재

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL REACTION-DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

Chunlai Mu|Dengming Liu|Shouming Zhou
대한수학회 (The Korean Mathematical Society)|2010.11|대한수학회지 (Journal of the KMS)|제47권 제6호|pp. 1317-1328

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

blow-upglobal existencereaction-diffusion equationnonlocal nonlinear boundary condition
주제분류수학

초록

In this paper, we study the properties of positive solutions for the reaction-diffusion equation [수식] with nonlocal nonlinear boundary condition u (x, t) =∫Ω∫ (x, y) ul (y, t)dy on □Ω×(0, T) and nonnegative initial data u0 (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

Abstract

In this paper, we study the properties of positive solutions for the reaction-diffusion equation [수식] with nonlocal nonlinear boundary condition u (x, t) =∫Ω∫ (x, y) ul (y, t)dy on □Ω×(0, T) and nonnegative initial data u0 (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

참고문헌 (20)

  1. S. Carl, "Generalized quasilinearization method for reactiondiffusion equations under nonlinear and nonlocal flux conditions", J. Math. Anal. Appl., 271(1), pp.182~205 (2002)
  2. D. E. Carlson, "Linear Thermoelasticity, in Encyclopedia of Physis" (1972), Springer
  3. 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)
  4. W. A. Day, "A decreasing property of solutions of parabolic equations with applications to thermoelasticity", Quart. Appl. Math., 40(4), pp.468~475 (1982)
  5. W. A. Day, "Heat Conduction within Linear Thermoelasticity", Springer Tracts in Natural Philosophy, 30 (1985), Springer-Verlag
  6. K. Deng, "Comparison principle for some nonlocal problems", Quart. Appl. Math., 50(3), pp.517~522 (1992)
  7. L. C. Evans, "Partial Differential Equations", Graduate Studies in Mathematics, 19 (1998), American Mathematical Society
  8. A. Friedman, "Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions", Quart. Appl. Math., 44(3), pp.401~407 (1986)
  9. A. Gladkov, "Blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition", J. Math. Anal. Appl., 338(1), pp.264~273 (2008)
  10. M. Jazar, "Blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions", Ann. Inst. H. Poincare Anal. Non Lineaire, 25(2), pp.215~218 (2008)
  11. J. Liang, "On a comparison principle for delay coupled systems with nonlocal and nonlinear boundary conditions, in press", ~
  12. Z. G. Lin, "Uniform blowup profiles for diffusion equations with nonlocal source and nonlocal boundary", Acta Math. Sci. Ser. B Engl. Ed., 24(3), pp.443~450 (2004)
  13. Q. L. Liu, "Blow-up for a degenerate parabolic equation with a nonlocal source", J. Math. Anal. Appl., 285(2), pp.487~505 (2003)
  14. C. M. Peng, "Blow-up for a degenerate parabolic equation with a nonlocal source", Appl. Math. Comput., 201(1), pp.250~259 (2008)
  15. A. El Soufi, "A gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions", Ann. Inst. H. Poincar´e Anal. Non Lineaire, 24(1), pp.17~39 (2007)
  16. P. Souplet, "Blow-up in nonlocal reaction-diffusion equations", SIAM J. Math. Anal., 29(6), pp.1301~1334 (1998)
  17. M. X. Wang, "Properties of positive solutions for non-local reactiondiffusion problems", Math. Methods Appl. Sci., 19(14), pp.1141~1156 (1996)
  18. Y. L. Wang, "Blowup of solutions to a porous medium equation with nonlocal boundary condition", Appl. Math. Comput., 192(2), pp.579~585 (2007)
  19. Y. L. Wang, "Properties of positive solution for nonlocal reaction-diffusion equation with nonlocal boundary", Bound. Value Probl., pp.12~ (2007)
  20. H. M. Yin, "On a class of parabolic equations with nonlocal boundary conditions", J. Math. Anal. Appl., 294(2), pp.712~728 (2004)

관련 논문AI추천

Some types of reaction-diffusion systems with nonlocal boundary conditionsWenjie Gao, Yuzhu Han대한수학회 · 대한수학회보2013 · 제50권 제6호Global 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 제3호ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS IN R^nBaishun Lai, Qing Luo, Shuqing Zhou대한수학회 · 대한수학회지2011 · 제48권 제2호Critical Fujita exponent for a fast diffusive equation with variable coefficientsChunlai Mu, Wanjuan Du, Zhongping Li대한수학회 · 대한수학회보2013 · 제50권 제1호Local 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 제1호

이 간행물의 다른 논문 (14건)

ON MIXED TWO-TERM EXPONENTIAL SUMSZhang Tianpingpp. 1107-1122EIGENVALUE PROBLEM OF BIHARMONIC EQUATION WITH HARDY POTENTIALYangxin Yao, Shaotong He, Qingtang Supp. 1123-1135ON THE GOODNESS OF FIT TEST FOR DISCRETELY OBSERVED SAMPLE FROM DIFFUSION PROCESSES: DIVERGENCE MEASURE APPROACH이상열pp. 1137-1146SPLITTING TYPE, GLOBAL SECTIONS AND CHERN CLASSES FOR TORSION FREE SHEAVES ON PNCristina Bertone, Margherita Roggeropp. 1147-1165HIGHER WEIGHTS AND GENERALIZED MDS CODES한성휴, Steven T. Doughertypp. 1167-1182
원문 보기