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Global solutions of the cooperative cross-fiffusion systems

심성아
한국수학교육학회|2015.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제22권 제1호|pp. 75-90

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참고문헌

키워드

crossdiffusion systemscooperative dynamicsexistence of global solutionsuniform bound
주제분류수학

초록

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of W_(1,2) norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

Abstract

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of W_(1,2) norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

참고문헌 (8)

  1. H. Amann, "Dynamic theory of quasilinear parabolic equations, III. Global Existence", Math Z, 202, pp.219~250 (1989)
  2. H. Amann, "Dynamic theory of quasilinear parabolic equations, II. Reaction-diffusion sys-tems", Differential and Integral Equations, 3, pp.13~75 (1990)
  3. Non-homogeneous linear and quasilinear elliptic and parabolic boundary value problems. Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992), "H. Amann", Teubner-Texte Math., 9~126 (1993)
  4. M. Delgado, "A Lotka-Volterra symbiotic model with cross-diffusion", J. Differential Equations, 246, pp.2131~2149 (2009)
  5. A. Friedman, "Partial differential equations" (1969), Holt, Rinehart and Winston
  6. L. Nirenberg, "On ellipic partial differential equations", Ann. Scuo. Norm. Sup. Pisa, 13(3), pp.115~162 (1959)
  7. A. Okubo, "Interdisciplinary Applied Mathematics, Vol. 14" (2001), Springer-Verlag
  8. C.V. Pao, "Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion", Nonlinear Anal, 60, pp.1197~1217 (2005)

관련 논문AI추천

CONVERGENCE RESULTS FOR THE COOPERATIVE CROSS-DIFFUSION SYSTEM WITH WEAK COOPERATIONS심성아한국수학교육학회 · 이론수학과 교직수학2017 · 제24권 제4호W½-estimates on the prey-predator systems with cross-diffusions and functional responses심성아대한수학회 · 대한수학회논문집2008 · 제23권 제2호Global Existence of Solutions to the Prey-Predator System with a Single Cross-Diffusion심성아대한수학회 · 대한수학회보2006 · 제43권 제2호Some types of reaction-diffusion systems with nonlocal boundary conditionsWenjie Gao, Yuzhu Han대한수학회 · 대한수학회보2013 · 제50권 제6호CRITICAL EXPONENTS FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUXBotao Chen, Chunlai Mu, Yongsheng Mi대한수학회 · 대한수학회지2011 · 제48권 제3호Global existence and blow-up for a degenerate reaction-diffusion system with nonlinear localized sources and nonlocal boundary conditionsFei Liang대한수학회 · 대한수학회지2016 · 제53권 제1호

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