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Autor:
Towne, Aaron, Dawson, Scott T. M., Brès, Guillaume A., Lozano-Durán, Adrián, Saxton-Fox, Theresa, Parthasarathy, Aadhy, Jones, Anya R., Biler, Hulya, Yeh, Chi-An, Patel, Het D., Taira, Kunihiko
We present a publicly accessible database designed to aid in the conception, training, demonstration, evaluation, and comparison of reduced-complexity models for fluid mechanics. Availability of high-quality flow data is essential for all of these as
Externí odkaz:
http://arxiv.org/abs/2206.11801
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
We construct radial self-similar solutions of the, so called, minimal parabolic-elliptic Keller--Segel model in several space dimensions with radial, nonnegative initial conditions with are below the Chandrasekhar solution -- the singular stationary
Externí odkaz:
http://arxiv.org/abs/2001.02571
Akademický článek
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Publikováno v:
In American Journal of Ophthalmology March 2023 247:88-95
Publikováno v:
In Journal of Differential Equations 25 January 2023 344:891-914
Autor:
Biler, Piotr, Pilarczyk, Dominika
We study the existence of global-in-time solutions for a nonlinear heat equation with nonlocal diffusion, power nonlinearity and suitably small data (either compared pointwisely to the singular solution or in the norm of a critical Morrey space). The
Externí odkaz:
http://arxiv.org/abs/1807.03567