Results 1 to 10 of about 221 (39)

Properties of generalized degenerate parabolic systems

Advances in Nonlinear Analysis, 2022
In this article, we consider the parabolic system (ui)t=∇⋅(mUm−1A(∇ui,ui,x,t)+ℬ(ui,x,t)),(1≤i≤k){({u}^{i})}_{t}=\nabla \cdot (m{U}^{m-1}{\mathcal{A}}(\nabla {u}^{i},{u}^{i},x,t)+{\mathcal{ {\mathcal B} }}({u}^{i},x,t)),\hspace{1.0em}(1\le i\le k) in the ...
Kim Sunghoon, Lee Ki-Ahm
doaj   +1 more source

Higher integrability for anisotropic parabolic systems of p-Laplace type

Advances in Nonlinear Analysis, 2023
In this article, we consider anisotropic parabolic systems of pp-Laplace type. The model case is the parabolic pi{p}_{i}-Laplace system ut−∑i=1n∂∂xi(∣Diu∣pi−2Diu)=0{u}_{t}-\mathop{\sum }\limits_{i=1}^{n}\frac{\partial }{\partial {x}_{i}}({| {D}_{i}u| }^{{
Mons Leon
doaj   +1 more source

Maximum principles for parabolic systems coupled in both first‐order and zero‐order terms

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 813-816, 1994., 1993
Some generalized maximum principles are established for linear second‐order parabolic systems in which both first‐order and zero‐order terms are coupled.
Chiping Zhou
wiley   +1 more source

Unstable periodic wave solutions of Nerve Axion diffusion equations

International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 4, Page 787-796, 1987., 1987
Unstable periodic solutions of systems of parabolic equations are studied. Special attention is given to the existence and stability of solutions.
Rina Ling
wiley   +1 more source

Liouville's theorem for the generalized harmonic function [PDF]

Anal. Math. Phys. 10 (2020), no. 4, 2018
In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.
arxiv   +1 more source

The higher integrability of weak solutions of porous medium systems

Advances in Nonlinear Analysis, 2018
In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.
Bögelein Verena, Duzaar Frank, Korte Riikka, Scheven Christoph   +3 more
doaj   +1 more source

On the Green's matrices of strongly parabolic systems of second order [PDF]

Indiana Univ. Math. J. 57 (2008) no. 4, pp. 1633--1678., 2007
We establish existence and various estimates of fundamental matrices and Green's matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical domains under the assumption that solutions of the systems satisfy an interior H\"{o}lder continuity estimate.
arxiv   +1 more source

System of degenerate parabolic p-Laplacian

Open Mathematics
In this article, we study the mathematical properties of the solution u=(u1,…,uk){\bf{u}}=({u}^{1},\ldots ,{u}^{k}) to the degenerate parabolic system ut=∇⋅(∣∇u∣p−2∇u),(p>2).{{\bf{u}}}_{t}=\nabla \hspace{0.25em}\cdot \hspace{0.25em}({| \nabla {\bf{u}}| }^
Kim Sunghoon, Lee Ki-Ahm
doaj   +1 more source

On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism

European Journal of Applied Mathematics
In this paper, we consider reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions.
Rachidi B. Salako, Yixiang Wu
doaj   +1 more source

Generalized result on the global existence of positive solutions for a parabolic reaction-diffusion model with an m × m diffusion matrix

Demonstratio Mathematica
The aim of this work is to study the global existence in time of solutions for the tridiagonal system of reaction-diffusion by order mm. Our techniques of proof are based on compact semigroup methods and some L1{L}^{1}-estimates.
Barrouk Nabila, Abdelmalek Karima
doaj   +1 more source