Results 51 to 60 of about 111 (109)

Analysis of a Darcy flow model with a dynamic pressure saturation relation

, 1998
We consider a new model for groundwater flow. The model differs from previous models in that the saturation-pressure relation is extended with a dynamic term, namely the time derivative of the saturation.
Josephus Hulshof, John R. King
core  

Boundedness and finite-time blow-up for the chemotaxis system with indirect signal production and flux limitation

Advances in Nonlinear Analysis
In this work, we consider a flux-limited chemotaxis model with indirect signal production and nonlinear diffusion,ut=∇⋅(D(u)∇u)−∇⋅(uf(|∇v|2)∇v)−k1u+k2w,x∈Ω,t>0,0=Δv−μ(t)+w,x∈Ω,t>0,wt=Δw−λ1w+λ2u,x∈Ω,t>0 $$\begin{cases}_{t}=\nabla \cdot \left(D\left(u ...
Tu Xinyu, Mu Chunlai, Minghua Zhang
doaj   +1 more source

Stabilization of arbitrary structures in a three-dimensional doubly degenerate nutrient taxis system

European Journal of Applied Mathematics
The doubly degenerate nutrient taxis system (0.1) \begin{equation} \left \{ \begin{aligned} &u_{t}=\nabla \cdot (uv\nabla u)-\chi \nabla \cdot (u^{\alpha }v\nabla v)+\ell uv,&x\in \Omega ,\, t\gt 0,\\[5pt] & v_{t}=\Delta v-uv,&x\in \Omega ,\, t\gt 0,\\
Xiang-Mao De-Ji, Ai Huang, Yifu Wang
doaj   +1 more source

DIFFUSION IN DEFORMABLE MEDIA

, 2008
. We begin with the initial-boundary-value problem for a coupled system of partial differential equations which describes the Biot consolidation model in poroelasticity.
R. E. Showalter
core  

Continuity of the temperature in a multi-phase transition problem. [PDF]

Math Ann, 2022
Gianazza U, Liao N.
europepmc   +1 more source

A Morphological Scheme For Mean Curvature Motion And Applications To Anisotropic Diffusion And Motion Of Level Sets.

, 1995
. This paper introduces a discrete scheme for mean curvature motion using a morphological image processing approach. After briefly presenting an axiomatic approach of image processing and the mean curvature PDE, the properties of the proposed scheme are ...
Georges Koepfler, Francine Catt
core  

Weak solutions for anisotropic parabolic equations with low-integrability initial data

Advances in Nonlinear Analysis
We study an anisotropic nonlinear parabolic equation with initial data u 0 ∈ L r(Ω), for 1 < r < 2, and a general Carathéodory lower-order term. The zero-order term is allowed to grow with a coefficient b(x, t) belonging to a suitable Lorentz space ...
Li Zhongqing
doaj   +1 more source

Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]

Calc Var Partial Differ Equ, 2021
Bögelein V, Heran A, Schätzler L, Singer T.   +3 more
europepmc   +1 more source

Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

Advanced Nonlinear Studies, 2017
The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time,
Hoang Luan T., Kieu Thinh T.
doaj   +1 more source

The Finite Speed of Propagation Property for the Thin Film Equation in Terms of the L&sup1;-Norm

, 2007
We consider the equation u t + (u n u xxx ) x = 0 with 0 ! n ! 3 and establish an estimate for the finite speed of propagation of the support of compactly supported nonnegative solutions.
Josephus Hulshof, Andrey Shishkov
core