CONVERGENCE RESULTS FOR THE COOPERATIVE CROSS-DIFFUSION SYSTEM WITH WEAK COOPERATIONS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-speci¯c competition pressures and the inter-speci¯c cooperative pres- sures dominated by intra-speci¯c competition pressures. Under these conditions the W1 2 -bound and the time global existence of the solution for the cooperative cross- diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.
Abstract
We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-speci¯c competition pressures and the inter-speci¯c cooperative pres- sures dominated by intra-speci¯c competition pressures. Under these conditions the W1 2 -bound and the time global existence of the solution for the cooperative cross- diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.
참고문헌 (10)
- H. Amann, "Dynamic theory of quasilinear parabolic equations, II. Reaction-diffusion systems", Differential and Integral Equations, 3(1), pp.13~75 (1990)
- A. Friedman, "Partial differential equations" (1969), Holt, Rinehart and Winston
- D. Gilbarg, "Elliptic Partial Differential Equations of Second Order" (1983), Springer-Verlag
- Y. Lou, "On the global existence of a cross-diffusion system", Discrete Contin. Dynam. Systems, 4(2), pp.193~203 (1998)
- L. Nirenberg, "On ellipic partial differential equations", Ann. Scuo. Norm. Sup. Pisa, 13(3), pp.115~162 (1959)
- A. Okubo, "Diffusion and Ecological Problems : Mathematical Models" (1980), Springer-Verlag
- M.H. Protter, "Maximum Principles in Differential Equations" (1967), Prentice-Hall Inc
- N. Shigesada, "Spatial segregation of interacting species", J. Theo. Biology, 79, pp.83~99 (1979)
- S. Shim, "Uniform boundedness and convergence of solutions to the system with cross-diffusions dominated by self-diffusions", Nonlinear Analysis: Real World Applications, 4, pp.65~86 (2003)
- 심성아, "Global solutions of the cooperative cross-fiffusion systems", 순수 및 응용수학, 22(1), pp.75~90 (2015), 한국수학교육학회