$\mathcal{W}$-Entropy formulae and differential Harnack estimates for porous medium equations on Riemannian manifolds [PDF]
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, Volume 17, Number 6,
November 2018, 2018 In this paper, we prove Perelman type $\mathcal{W}$-entropy formulae and global differential Harnack estimates for positive solutions to porous medium equation on the closed Riemannian manifolds with Ricci curvature bounded below. As applications, we derive Harnack inequalities and Laplacian estimates.
arxiv +1 more source
Evolutionary quasi-variational and variational inequalities with constraints on the derivatives
Advances in Nonlinear Analysis, 2018 This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial ...
Miranda Fernando +2 more
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 +9 more
doaj +1 more source
Advances in Nonlinear AnalysisThis article is concerned with the qualitative properties for the Cauchy problem of a non-Newtonian filtration equation with a reaction source term and volumetric moisture content.
Huo Wentao, Fang Zhong Bo
doaj +1 more source
On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation
Alexandria Engineering Journal, 2020 In this paper, we are interested in finding the function u(t,x),(t,x)∈[0,T)×Ω from the final data u(T,x)=ϕ(x), satisfies a nonhomogeneous fractional pseudo-parabolic equation. The problem is stable for the cases σν, the problem is ill-posed (in the sense
Nguyen Hoang Luc +3 more
doaj
$C^{1, α}$-regularity for functions in solution classes and its application to parabolic normalized $p$-Laplace equations [PDF]
arXiv, 2023 We establish the global $C^{1, \alpha}$-regularity for functions in solution classes, whenever ellipticity constants are sufficiently close. As an application, we derive the global regularity result concerning the parabolic normalized $p$-Laplace equations, provided that $p$ is close to 2.
arxiv
Porosity of the Free Boundary in the Singular p-Parabolic Obstacle Problem [PDF]
arXiv, 2015 In this paper we establish the exact growth of the solution of the singular quasilinear p-parabolic obstacle problem near the free boundary from which we deduce its porosity.
arxiv
On the Time Derivative in a Quasilinear Equation [PDF]
Trans. R. Norw. Soc. Sci. Lett. 2008(2), 1-7, 2016 The time derivative (in the sense of distributions) of the solutions to the Evolutionary p-Laplace Equation is proved to be a function in a local Lebesgue space.
arxiv
A priori bounds for degenerate and singular evolutionary partial integro-differential equations [PDF]
arXiv, 2010 We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these ...
arxiv
Total Variation Flow and Sign Fast Diffusion in one dimension [PDF]
arXiv, 2011 We consider the dynamics of the Total Variation Flow (TVF) $u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\Delta\sign(u)$ in one spatial dimension. We find the explicit dynamic and sharp asymptotic behaviour for the TVF, and we deduce the one for the SFDE by an explicit correspondence between the two equations.
arxiv