Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Boritchev, Alexandre"'
We study two toy models obtained after a slight modification of the nonlinearity of the usual doubly parabolic Keller-Segel system. For these toy models, both consisting of a system of two parabolic equations, we establish that for data which are, in
Externí odkaz:
http://arxiv.org/abs/2206.10399
We study the global existence of the parabolic-parabolic Keller-Segel system in $\R^d , d \ge 2$. We prove that initial data of arbitrary size give rise to global solutions provided the diffusion parameter $\tau$ is large enough in the equation for t
Externí odkaz:
http://arxiv.org/abs/2203.09130
We consider the drift-diffusion equation $u_t-\epsilon\Delta u + \nabla \cdot(u\nabla K^*u)=0$ in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we restrict ourselves to the model case $K(x)=-|x|$. We qua
Externí odkaz:
http://arxiv.org/abs/2009.12173
We consider the drift-diffusion equation $$ u_t-\varepsilon \Delta u+\nabla\cdot(u\nabla K\star u)=0 $$ in the whole space with global-in-time bounded solutions. Mass concentration phenomena for radially symmetric solutions of this equation with smal
Externí odkaz:
http://arxiv.org/abs/2001.06218
Publikováno v:
J. Math. Phys. 62 (2021), 093101
Riemann's non-differentiable function is one of the most famous examples of continuous but nowhere differentiable functions, but it has also been shown to be relevant from a physical point of view. Indeed, it satisfies the Frisch-Parisi multifractal
Externí odkaz:
http://arxiv.org/abs/1910.13191
Publikováno v:
In Journal of Differential Equations 25 January 2023 344:891-914
Autor:
Boritchev, Alexandre
We consider the fractional unforced Burgers equation in the one-dimensional space-periodic setting: $$\partial u/\partial t+(f(u))_x +\nu \Lambda^{\alpha} u= 0, t \geq 0,\ \mathbb{x} \in \mathbb{T}^d=(\mathbb{R}/\mathbb{Z})^d.$$ Here $f$ is strongly
Externí odkaz:
http://arxiv.org/abs/1608.01460
Autor:
Boritchev, Alexandre
We prove exponential convergence to the stationary measure for a class of 1d Lagrangian systems with random forcing in the space-periodic setting: $$ \phi_t+\phi_x^2/2=F^{\omega}, x \in S^1 = \mathbb{R}/\mathbb{Z}. $$ This confirms a part of a conjec
Externí odkaz:
http://arxiv.org/abs/1601.01937
Autor:
Boritchev, Alexandre
Cette thèse traite du comportement des solutions u de l'équation de Burgers généralisée sur le cercle: u_t+f'(u)u_x=\nu u_{xx}+\eta,\ x \in S^1=\R/\Z. Ici, f est lisse, fortement convexe et satisfait certaines conditions de croissance. La consta
Externí odkaz:
http://pastel.archives-ouvertes.fr/pastel-00739791
http://pastel.archives-ouvertes.fr/docs/00/73/97/91/PDF/ThA_se_fichier_principal.pdf
http://pastel.archives-ouvertes.fr/docs/00/73/97/91/PDF/ThA_se_fichier_principal.pdf
Publikováno v:
In Journal of Differential Equations 15 January 2021 271:1092-1108