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pro vyhledávání: '"Heihoff, Frederic"'
Autor:
Heihoff, Frederic
We consider the chemotaxis-consumption system \[ \left\{ \begin{aligned} u_t &= \Delta u - \chi \nabla \cdot (u\nabla v) \\ v_t &= \Delta v - uv \end{aligned} \right. \] in a smooth bounded domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 2$, with par
Externí odkaz:
http://arxiv.org/abs/2308.14934
Autor:
Heihoff, Frederic
We prove two new functional inequalities of the forms\[ \int_G \varphi (\psi - \overline{\psi}) \leq \frac{1}{a}\int_G \psi \ln \left(\frac{\;\psi\;}{ \overline{\psi}}\right) + \frac{a}{4\beta_0} \left\{ \int_G \psi \right\}\int_G|\nabla \varphi|^2 \
Externí odkaz:
http://arxiv.org/abs/2211.00624
Autor:
Heihoff, Frederic
It has been well established that, in attraction-repulsion Keller-Segel systems of the form\begin{equation*} \left\{ \begin{aligned} u_t &= \Delta u - \chi \nabla \cdot (u\nabla v) + \xi \nabla \cdot (u\nabla w), \\ \tau v_t &= \Delta v + \alpha u -
Externí odkaz:
http://arxiv.org/abs/2210.12208
Autor:
Heihoff, Frederic, Yokota, Tomomi
The diffusive Lotka-Volterra predator-prey model \begin{eqnarray*} \left\{ \begin{array}{rcll} u_t &=& \nabla\cdot \left[ d_1\nabla u + \chi v^2 \nabla \Big(\dfrac{u}{v}\Big)\right] +u(m_1-u+av), \qquad & x\in\Omega, \ t>0, \\ v_t &=& d_2\Delta v+v(m
Externí odkaz:
http://arxiv.org/abs/2203.13958
Autor:
Heihoff, Frederic
We consider the potentially degenerate haptotaxis system \begin{equation*} \left\{ \begin{aligned} u_t &= \nabla \cdot (\mathbb{D} \nabla u + u \nabla \cdot \mathbb{D}) - \chi \nabla \cdot (u\mathbb{D}\nabla w) + \mu u(1-u^{r- 1}), \\ w_t &= - uw \en
Externí odkaz:
http://arxiv.org/abs/2202.07112
Autor:
Fuest, Mario, Heihoff, Frederic
We show that spatial patterns ("hotspots") may form in the crime model \begin{equation} \left\{\; \begin{aligned} u_{t} &= \tfrac{1}{\varepsilon}\Delta u - \tfrac{\chi}{\varepsilon} \nabla \cdot \left(\tfrac{u}{v} \nabla v \right) - \varepsilon uv, \
Externí odkaz:
http://arxiv.org/abs/2109.01016
Autor:
Heihoff, Frederic
We consider the parabolic-elliptic Keller-Segel system \[ \left\{ \begin{aligned} u_t &= \Delta u - \chi \nabla \cdot (u \nabla v), \\ 0 &= \Delta v - v + u \end{aligned} \right. \tag{$\star$} \] in a smooth bounded domain $\Omega \subseteq \mathbb{R
Externí odkaz:
http://arxiv.org/abs/2006.09345
Autor:
Heihoff, Frederic
We consider the system \[ \left\{ \begin{aligned} u_t &= \Delta u - \chi \nabla \cdot ( \tfrac{u}{v} \nabla v) - uv + \rho u - \mu u^2, \\ v_t &= \Delta v - v + u v \end{aligned} \right. \tag{$\star$} \] with $\rho \in \mathbb{R}, \mu > 0, \chi > 0$
Externí odkaz:
http://arxiv.org/abs/1911.04838
Autor:
Heihoff, Frederic
We study the chemotaxis-Navier-Stokes system \[\left\{\; \begin{aligned} n_t + u\cdot\nabla n &=\Delta n - \nabla\cdot (nS(x,n,c)\nabla c), &&x\in\Omega, t > 0, \\ c_t + u\cdot\nabla c &=\Delta c - n f(c), && x\in \Omega, t > 0, \\ u_t + (u\cdot\nabl
Externí odkaz:
http://arxiv.org/abs/1908.11282
Autor:
Heihoff, Frederic, Yokota, Tomomi
Publikováno v:
In Nonlinear Analysis: Real World Applications February 2023 69