Results 11 to 20 of about 272 (36)

Global analytic expansion of solution for a class of linear parabolic systems with coupling of first order derivatives terms [PDF]

, 2009
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time.
Kampen, Joerg
core   +2 more sources

The parabolic-parabolic Keller-Segel system with critical diffusion as a gradient flow in $\RR^d$, $d \ge 3$ [PDF]

, 2012
It is known that, for the parabolic-elliptic Keller-Segel system with critical porous-medium diffusion in dimension $\RR^d$, $d \ge 3$ (also referred to as the quasilinear Smoluchowski-Poisson equation), there is a critical value of the chemotactic ...
Blanchet, Adrien, Laurençot, Philippe
core   +5 more sources

A Note on Doubly Nonlinear Parabolic Systems with Unilateral Constraint

, 2011
We prove the existence and uniqueness of the solution to the doubly nonlinear parabolic systems with mixed boundary conditions. Due to the unilateral constraint the problem comes as a variational inequality.
Beneš, Michal
core   +1 more source

A gradient flow approach to a thin film approximation of the Muskat problem [PDF]

, 2011
A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second ...
Laurencot, Philippe, Matioc, Bogdan-Vasile   +1 more
core   +5 more sources

Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients

, 2007
Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $\mathbb{R}^n$.
Kim, Seick
core   +2 more sources

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

Local pinching estimates in 3-dim Ricci flow

, 2013
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these ...
Chen, Bing-Long, Xu, Guoyi, Zhang, Zhuhong   +2 more
core   +1 more source

Finite time blowup for parabolic systems in two dimensions

, 2016
We construct examples of finite time singularity from smooth data for linear uniformly parabolic systems in the plane. We obtain similar examples for quasilinear systems with coefficients that depend only on the solution.Comment: 16 ...
Mooney, Connor
core   +1 more source