Results 41 to 50 of about 91 (91)

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

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

Math Ann, 2022
Gianazza U, Liao N.
europepmc   +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

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

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

Ireneo Peral: Forty Years as Mentor

Advanced Nonlinear Studies, 2017
In this article we present a survey of the Ph.D. theses that have been completed under the advice of Ireneo Peral.Following a chronological order, we summarize the main results contained in the works of the former students of Ireneo Peral.
Abdellaoui Boumediene, Aguilar Juan Antonio, Barrios Begoña, Colorado Eduardo, Charro Fernando, García Azorero Jesús, Medina Maria, Merchán Susana, Montoro Luigi, Primo Ana   +9 more
doaj   +1 more source

On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient

Electronic Journal of Differential Equations, 2002
We study the Cauchy problem for the nonlinear (possibly strongly) degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(x)f(u))=partial_x^2 A(u), quad A'(cdot)ge 0, $$ where the coefficient $gamma(x)$ is possibly ...
John D. Towers, Nils H. Risebro, Kenneth H. Karlsen   +2 more
doaj  

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

Existence of solutions to a diffusive shallow medium equation. [PDF]

J Evol Equ, 2021
Bögelein V, Dietrich N, Vestberg M.
europepmc   +1 more source