Kinetic and Related Models: latest papers Latest articles for selected journal Fractional diffusion limit of a linear kinetic equation in a bounded domain Pedro Aceves-Sánchez and Christian Schmeiser Fri, 1 Sep 2017 20:00:00 GMT Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime Weizhu Bao, Loïc Le Treust and Florian Méhats Fri, 1 Sep 2017 20:00:00 GMT Upper Maxwellian bounds for the Boltzmann equation with pseudo-Maxwell molecules Alexander V. Bobylev and Irene M. Gamba Fri, 1 Sep 2017 20:00:00 GMT Blow-up, steady states and long time behaviour of excitatory-inhibitory nonlinear neuron models María J. Cáceres and Ricarda Schneider Fri, 1 Sep 2017 20:00:00 GMT Numerical study of a particle method for gradient flows José Antonio Carrillo, Yanghong Huang, Francesco Saverio Patacchini and Gershon Wolansky Fri, 1 Sep 2017 20:00:00 GMT Asymptotic preserving and time diminishing schemes for rarefied gas dynamic Nicolas Crouseilles, Giacomo Dimarco and Mohammed Lemou Fri, 1 Sep 2017 20:00:00 GMT Finite range method of approximation for balance laws in measure spaces Piotr Gwiazda, Piotr Orlinski and Agnieszka Ulikowska Fri, 1 Sep 2017 20:00:00 GMT Emergent dynamics in the interactions of Cucker-Smale ensembles Seung-Yeal Ha, Dongnam Ko, Yinglong Zhang and Xiongtao Zhang Fri, 1 Sep 2017 20:00:00 GMT Fractional kinetic hierarchies and intermittency Anatoly N. Kochubei and Yuri Kondratiev Fri, 1 Sep 2017 20:00:00 GMT Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces Fucai Li, Yanmin Mu and Dehua Wang Fri, 1 Sep 2017 20:00:00 GMT Decay property for solutions to plate type equations with variable coefficients Shikuan Mao and Yongqin Liu Fri, 1 Sep 2017 20:00:00 GMT On a linear runs and tumbles equation Stéphane Mischler and Qilong Weng Fri, 1 Sep 2017 20:00:00 GMT Kinetic models for traffic flow resulting in a reduced space of microscopic velocities Gabriella Puppo, Matteo Semplice, Andrea Tosin and Giuseppe Visconti Fri, 1 Sep 2017 20:00:00 GMT Boundedness and large time behavior of an attraction-repulsion chemotaxis model with logistic source 0,\\ v_{t}=\Delta v+\alpha u-\beta v, &x\in\Omega,\ t>0,\\ w_{t}=\Delta w+\gamma u-\delta w, &x\in\Omega,\ t>0,\\ \end{cases} \end{equation} in a smooth bounded domain $\Omega \subset \mathbb{R}^n(n\geq 1)$, with homogeneous Neumann boundary conditions and nonnegative initial data $(u_0,v_0,w_0)$ satisfying suitable regularity, where $\chi\geq 0,\xi\geq 0,\alpha, \beta, \gamma, \delta>0$ and $f$ is a smooth growth source satisfying $f(0)\geq 0$ and $$f(u)\leq a-bu^\theta, \ \ u\geq 0,\ \ \mathrm{with~some} \ \ a\geq 0,b>0,\theta\geq1.$$ When $\chi\alpha=\xi\gamma$ (i.e. repulsion cancels attraction), the boundedness of classical solution of system (∗) is established if the dampening parameter $\theta$ and the space dimension $n$ satisfy \begin{equation*} \begin{cases} \theta > \max\{1,3-\frac6n\}, &\text{when }\ \ 1\leq n\leq 5,\\ \theta\geq 2, &\text{when }\ \ 6\leq n\leq 9,\\ \theta>1+\frac{2(n-4)}{n+2}, &\text{when} \ \ \ n\geq10.\\ \end{cases} \end{equation*} Furthermore, when $f(u)=\mu u(1-u)$ and repulsion cancels attraction, by constructing appropriate Lyapunov functional, we show that if $\mu>\frac{\chi^2\alpha^2(\beta-\delta)^2}{8\delta\beta^2}$, the solution $(u,v,w)$ exponentially stabilizes to the constant stationary solution $(1,\frac{\alpha}{\beta},\frac{\gamma}{\delta})$ in the case of $1\leq n\leq 9$. Our results implies that when repulsion cancels attraction the logistic source play an important role on the solution behavior of the attraction-repulsion chemotaxis system. ]]> Shijie Shi, Zhengrong Liu and Hai-Yang Jin Fri, 1 Sep 2017 20:00:00 GMT