Anisotropic 𝑝-Laplacian evolution of fast diffusion type

F Feo, JL Vázquez, B Volzone - Advanced Nonlinear Studies, 2021‏ - degruyter.com
We study an anisotropic, possibly non-homogeneous version of the evolution 𝑝-Laplacian
equation when fast diffusion holds in all directions. We develop the basic theory and prove …

[HTML][HTML] The very singular solution for the Anisotropic Fast Diffusion Equation and its consequences

JL Vázquez - Nonlinear Analysis, 2024‏ - Elsevier
Abstract We construct the Very Singular Solution (VSS) for the Anisotropic Fast Diffusion
Equation (AFDE) in the suitably good exponent range. VSS is a solution that, starting from …

[HTML][HTML] Anisotropic fast diffusion equations

F Feo, JL Vázquez, B Volzone - Nonlinear Analysis, 2023‏ - Elsevier
We prove the existence of self-similar fundamental solutions (SSF) of the anisotropic porous
medium equation in the suitable fast diffusion range. Each of such SSF solutions is uniquely …

Ginzburg–Landau vortex and mean curvature flow with external force field

HY Jian, YN Liu - Acta Mathematica Sinica, 2006‏ - Springer
This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a
parabolic Ginzburg–Landau system which simulates inhomogeneous type II …

Removability conditions for anisotropic parabolic equations in a computational validation

D Langemann, M Savchenko - Frontiers in Applied Mathematics and …, 2024‏ - frontiersin.org
The article investigates removability conditions for singularities of anisotropic parabolic
equations and in particular for the anisotropic porous medium equation and it aims in the …

Asymptotic behaviour of solutions and free boundaries of the anisotropic slow diffusion equation

F Feo, JL Vázquez, B Volzone - arxiv preprint arxiv:2412.12295, 2024‏ - arxiv.org
In this paper we explore the theory of the anisotropic porous medium equation in the slow
diffusion range. After revising the basic theory, we prove the existence of self-similar …

Solutions of the anisotropic porous medium equation in Rn under an l1-initial value

H Jian, B Song - Nonlinear Analysis: Theory, Methods & Applications, 2006‏ - Elsevier
Consider the anisotropic porous medium equation,[Formula: see text], where mi> 0,(i= 1,
2,…, n) satisfying max1⩽ i⩽ n {mi}⩽ 1,∑ i= 1nmi> n-2, and max1⩽ i⩽ n {mi}⩽ 1/n (2+∑ i …

Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations

E Henriques, S Ciani - arxiv preprint arxiv:2309.05023, 2023‏ - arxiv.org
In this work we are interested in the study of a class of anisotropic porous medium-type
equations whose prototype is\[u_t=\sum_ {i= 1}^ N\left (m_i u^{m_i-1} u_ {x_i}\right) …

A brief note on Harnack-type estimates for singular parabolic nonlinear operators

E Henriques, S Ciani - Bruno Pini Mathematical …, 2023‏ - mathematicalanalysis.unibo.it
A BRIEF NOTE ON HARNACK-TYPE ESTIMATES FOR SINGULAR PARABOLIC
NONLINEAR OPERATORS ——————– UNA BREVE NOTA SU DISUGU Page 1 A …

Propagation property for anisotropic nonlinear diffusion equation with convection

TS Khin, N Su - Journal of mathematical analysis and applications, 2009‏ - Elsevier
We consider propagation property for anisotropic diffusion equation with convection in 2
dimension, where p1, p2, m, α> 0. Among the results, we show that perturbation for the …