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In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order $s\in(0,2)$. It is proved that for $s>2p_{0}$, where $p_{0}$ is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.
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참고문헌 (49)
참고문헌 신청
Yago Ascasibar / 2013 / An approximate treatment of gravitational collapse / Physica D: Nonlinear Phenomena 262:71~82
N. Bellomo / 2015 / Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues / Mathematical Models and Methods in Applied Sciences 25(09):1663~1763
Piotr Biler / 2017 / Local criteria for blowup in two-dimensional chemotaxis models / Discrete & Continuous Dynamical Systems - A 37(4):1841~1856
Piotr Biler / 2013 / Blowup in higher dimensional two species chemotactic systems / Communications on Pure and Applied Analysis 12(1):89~98
Piotr Biler / 2012 / Blowup and self-similar solutions for two-component drift–diffusion systems / Nonlinear Analysis: Theory, Methods & Applications 75(13):5186~5193
N. Bellomo / 2015 / Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues / Mathematical Models and Methods in Applied Sciences 25(09):1663~1763
Piotr Biler / 2017 / Local criteria for blowup in two-dimensional chemotaxis models / Discrete & Continuous Dynamical Systems - A 37(4):1841~1856
Piotr Biler / 2013 / Blowup in higher dimensional two species chemotactic systems / Communications on Pure and Applied Analysis 12(1):89~98
Piotr Biler / 2012 / Blowup and self-similar solutions for two-component drift–diffusion systems / Nonlinear Analysis: Theory, Methods & Applications 75(13):5186~5193
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