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Long-time Properties of Prey-Predator System with Cross-Diffusion

심성아
대한수학회 (The Korean Mathematical Society)|2006.04|대한수학회논문집 (Communications of the KMS)|제21권 제2호|pp. 293-320

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주제분류수학

초록

Abstract

Using calculus inequalities and embedding theorems in R^1, weestablish W^1_2-estimates for the solutions of prey-predatorpopulation model with cross-diffusion and self-diffusion terms.Two cases are considered ; (i) d_1=d_2, al_{12}=al_{21}=0,and (ii) 0<al_{21}<8al_{11}, 0<al_{12}<8al_{22}. It isproved that solutions are bounded uniformly pointwise, and thatthe uniform bounds remain independent of the growth of thediffusion coefficient in the system. Also, convergence results areobtained when trightarrowinfty via suitable Liapunovfunctionals.

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관련 논문AI추천

Global Existence of Solutions to the Prey-Predator System with a Single Cross-Diffusion심성아대한수학회 · 대한수학회보2006 · 제43권 제2호Positive coexistence for a simple food chain model with ratio-dependent functional response and cross-diffusion고원률, 안인경대한수학회 · 대한수학회논문집2006 · 제21권 제4호W½-estimates on the prey-predator systems with cross-diffusions and functional responses심성아대한수학회 · 대한수학회논문집2008 · 제23권 제2호CONVERGENCE RESULTS FOR THE COOPERATIVE CROSS-DIFFUSION SYSTEM WITH WEAK COOPERATIONS심성아한국수학교육학회 · 이론수학과 교직수학2017 · 제24권 제4호STATIONARY PATTERNS FOR A PREDATOR-PREY MODEL WITH HOLLING TYPE Ⅲ RESPONSE FUNCTION AND CROSS-DIFFUSIONJia Liu, Zhigui Lin대한수학회 · 대한수학회보2010 · 제47권 제2호The asymptotic stability behavior in a Lotka-Volterra type Predator-Prey system고윤희대한수학회 · 대한수학회보2006 · 제43권 제3호

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