Results 41 to 50 of about 884 (117)

The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in L1

Advances in Nonlinear Analysis, 2019
In bounded n-dimensional domains Ω, the Neumann problem for the parabolic ...
Winkler Michael
doaj   +1 more source

Asymptotic behavior of global mild solutions to the Keller-Segel-Navier-Stokes system in Lorentz spaces

Advances in Nonlinear Analysis
The Keller-Segel-Navier-Stokes system in RN{{\mathbb{R}}}^{N} is considered, where N≥3N\ge 3. We show the existence and uniqueness of local mild solutions for arbitrary initial data and gravitational potential in scaling invariant Lorentz spaces ...
Takeuchi Taiki
doaj   +1 more source

An Energetic Variational Approach for ion transport

, 2014
The transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system.
Liu, Chun, Sheng, Ping, Xu, Shixin
core   +2 more sources

A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns

bioRxiv
Cell sorting by differential adhesion is one of the basic mechanisms explaining spatial organization of neurons in early stage brain development of fruit flies.
José A. Carrillo, Hideki Murakawa, Makoto Sato, Miaoxing Wang   +3 more
semanticscholar   +1 more source

Global-in-time behavior of the solution to a Gierer-Meinhardt system [PDF]

, 2012
Gierer-Meinhardt system is a mathematical model to describe biological pattern formation due to activator and inhibitor. Turing pattern is expected in the presence of local self-enhancement and long-range inhibition.
Karali, Georgia D, Suzuki, Takashi, Yamada, Yoshio   +2 more
core  

Boundedness and exponential convergence of a chemotaxis model for tumor invasion

, 2016
We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=\Delta u-\nabla \cdot(u\nabla v),& x\in\Omega, t>0,\\ v_t=\Delta v+wz,& x\in\Omega, t>0,\\ w_t=-wz,& x\in\Omega, t>0,\\ z_t=\Delta z-z+u, & x\in\Omega,
Jin, Haiyang, Xiang, Tian
core   +1 more source

Phase Transitions for the Brusselator Model

, 2010
Dynamic phase transitions of the Brusselator model is carefully analyzed, leading to a rigorous characterization of the types and structure of the phase transitions of the model from basic homogeneous states.
Ma T., Ma T., Shouhong Wang, Tian Ma
core   +1 more source

Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant

, 2015
We study nonnnegative radially symmetric solutions of the parabolic-elliptic Keller-Segel whole space system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=\Delta u-\nabla\!\cdot(u\nabla v),\ &x\in\mathbb{R}^n,& t>0,\\ 0 &=\Delta v+u ...
Black, Tobias
core   +1 more source

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source

Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics

European Journal of Applied Mathematics
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements.
Maryam Ahmadpoortorkamani, Alexei Cheviakov   +1 more
doaj   +1 more source