Results 31 to 40 of about 883 (118)

A PDE approach of inflammatory phase dynamics in diabetic wounds

, 2014
The objective of the present paper is the modeling and analysis of the dynamics of macrophages and certain growth factors in the inammatory phase, the rst one of the wound healing process.
N. Cónsul, S. Oliva, M. Pellicer
semanticscholar   +1 more source

Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “
Ion Stelian, Cruceanu Stefan-Gicu, Marinescu Dorin   +2 more
doaj   +1 more source

Necrotic tumor growth: an analytic approach

, 2012
The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium.
A Friedman, A Friedman, A Friedman, A Friedman, AH Kyle, D Gilbarg, F Zhou, H Byrne, J Escher, J Ward, JB Kim, Martin Kohlmann, MG Crandall, S Cui, W Müller-Klieser   +14 more
core   +1 more source

Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain [PDF]

, 2014
In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex.
Jiang, Jie, Wu, Hao, Zheng, Songmu
core  

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 degenerate migration-consumption model in domains of arbitrary dimension

Advanced Nonlinear Studies
In a smoothly bounded convex domain Ω⊂Rn ${\Omega}\subset {\mathbb{R}}^{n}$ with n ≥ 1, a no-flux initial-boundary value problem forut=Δuϕ(v),vt=Δv−uv, $$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv ...
Winkler Michael
doaj   +1 more source

A simple derivation of BV bounds for inhomogeneous relaxation systems [PDF]

, 2014
We consider relaxation systems of transport equations with heterogeneous source terms and with boundary conditions, which limits are scalar conservation laws. Classical bounds fail in this context and in particular BV estimates.
Perthame, Benoit, Seguin, Nicolas, Tournus, Magali   +2 more
core   +2 more sources

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

Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks

Advances in Nonlinear Analysis
The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the ...
Li Bin
doaj   +1 more source

Protection Zones in Periodic-Parabolic Problems

Advanced Nonlinear Studies, 2020
This paper characterizes whether or ...
López-Gómez Julián
doaj   +1 more source