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
Modelling adhesion-independent cell migration [PDF]
, 2020 A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force.
Jankowiak, Gaspard +4 more
core +5 more sources
From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem [PDF]
, 2014 The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of $N$ player games. Analysis of Nash equilibria is however a complex issue when the number of players is large.
Blanchet, Adrien, Carlier, Guillaume
core +6 more sources
Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs [PDF]
, 2005 This paper discusses the algorithms and implementations of three MATHEMATICA packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs.
Baldwin, D., Hereman, W., Sayers, J.
core +1 more source
A hyperbolic system and the cost of null controllability for the Stokes system [PDF]
, 2014 This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method we show that the cost of driving the Stokes system to rest at time T is of order e^C/T when T -->0^+,i.e., the same order as
Chaves-Silva, F. W.
core +5 more sources
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 +3 more
doaj +1 more source
Fractional diffusion in Gaussian noisy environment [PDF]
, 2015 We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic partial equations of the following form: $D_t^\alpha u(t, x)=\textit{B}u+u\cdot W^H$, where $D_t^\alpha$ is the fractional derivative of ...
Hu, Guannan, Hu, Yaozhong
core +3 more sources
On nonexistence of Baras--Goldstein type for higher-order parabolic equations with singular potentials [PDF]
, 2009 An analogy of nonexistence result by Baras and Goldstein (1984), for the heat equation with inverse singular potential, is proved for 2mth-order linear parabolic equations with Hardy-supercritical singular potentials.
Galaktionov, V. A., Kamotski, I. V.
core +4 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 +6 more sources