Zobrazeno 1 - 10
of 318
pro vyhledávání: '"Laurencot, Philippe"'
Autor:
Jiang, Jie, Laurençot, Philippe
A fully parabolic chemotaxis model of Keller-Segel type with local sensing is considered. The system features a signal-dependent asymptotically non-degenerate motility function, which accounts for a repulsion-dominated chemotaxis. Global boundedness
Externí odkaz:
http://arxiv.org/abs/2411.11430
Consider $m\>1$, $N\ge 1$ and $\max\{-2,-N\}\<\sigma\<0$. The Hardy-H\'enon equation with sublinear absorption\begin(equation*}- \Delta v(x) - |x|^\sigma v(x) + \frac{1}{m-1} v^{1/m}(x)= 0, \qquad x\in\mathbb{R}^N,\end{equation*}is shown to have at l
Externí odkaz:
http://arxiv.org/abs/2410.05909
Existence of a specific family of \emph{eternal solutions} in exponential self-similar form is proved for the following porous medium equation with strong absorption $$\partial_t u-\Delta u^m+|x|^{\sigma}u^q = 0 \;\;\text{ in }\;\; (0,\infty)\times\m
Externí odkaz:
http://arxiv.org/abs/2408.02466
Autor:
Laurençot, Philippe
Existence of global mild solutions to the infinite dimensional Redner--ben-Avraham--Kahng cluster system is shown without growth or structure condition on the kinetic coefficients, thereby extending previous results in the literature. The key idea is
Externí odkaz:
http://arxiv.org/abs/2408.02465
The well-posedness of the growth-coagulation equation is established for coagulation kernels having singularity near the origin and growing atmost linearly at infinity. The existence of weak solutions is shown by means of the method of the characteri
Externí odkaz:
http://arxiv.org/abs/2408.02457
Ranges of the real-valued parameters $\alpha$, $a$, $b$, and $m$ are identified for which the operator $$\mathcal{A}_{\alpha}(a,b)f(x):=x^\alpha\left(f''(x)+\frac{a}{x}f'(x)+\frac{b}{x^2}f(x)\right), \quad x>0,$$ generates an analytic semigroup in $L
Externí odkaz:
http://arxiv.org/abs/2406.16389
Solutions in self-similar form presenting finite time extinction to the singular diffusion equation with gradient absorption $$\partial_t u - \mathrm{div}(|\nabla u|^{p-2}\nabla u) +|\nabla u|^{q}=0 \qquad {\rm in} \ (0,\infty)\times\mathbb{R}^N$$ ar
Externí odkaz:
http://arxiv.org/abs/2406.11518
Autor:
Laurençot, Philippe, Trescases, Ariane
Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic diffusion rate $\phi$ dominates the inverse of the chemotactic motility function $\gamma$, in th
Externí odkaz:
http://arxiv.org/abs/2404.12166
Autor:
Hosono, Tatsuya, Laurençot, Philippe
Global existence and boundedness of solutions to the Cauchy problem for the four dimensional fully parabolic chemotaxis system with indirect signal production are studied. We prove that solutions with initial mass below $(8\pi)^2$ exist globally in t
Externí odkaz:
http://arxiv.org/abs/2404.01724
Publikováno v:
Nonlinearity, 2024, 37, pp.105007
Convergence of solutions to a partially diffusive chemotaxis system with indirect signal production and phenotype switching is shown in a two-dimensional setting when the switching rate increases to infinity, thereby providing a rigorous justificatio
Externí odkaz:
http://arxiv.org/abs/2403.13402