Results 71 to 80 of about 1,990 (139)

Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays

, 2015
In this paper, we consider functionals based on moments and non-linear entropies which have a linear growth in time in case of source-type so-lutions to the fast diffusion or porous medium equations, that are also known as Barenblatt solutions.
Dolbeault, Jean, Toscani, Giuseppe
core   +2 more sources

Very singular solutions for the thin film equation with absorption [PDF]

arXiv, 2009
Self-similar large time behaviour of weak solutions of the fourth-order parabolic thin film equations with absorption is studued.
arxiv  

An algorithm for one-dimensional Generalized Porous Medium Equations: interface tracking and the hole filling problem [PDF]

arXiv, 2014
Based on results of E. DiBenedetto and D. Hoff we propose an explicit finite difference scheme for the one dimensional Generalized Porous Medium Equation $\partial_t u=\partial_{xx}^2 \Phi(u)$. The scheme allows to track the moving free boundaries and captures the hole filling phenomenon when two free boundaries collide. We give an abstract convergence
arxiv  

Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator

Open Mathematics
In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator.
Dukenbayeva Aishabibi
doaj   +1 more source

Regularity for solutions of the two-phase Stefan problem [PDF]

arXiv, 2005
We consider local solutions of the two-phase Stefan problem with a "mushy" region. We show that if a (distributional) solution u is locally square integrable then the temperature is continuous.
arxiv  

The global solution of a diffusion equation with nonlinear gradient term

, 2013
Consider the viscosity solution to the initial boundary value problem of the diffusion equation ut=div(|∇um|p−2∇um)−uq1m|∇um|p1, with p>1, m>0, p1≤2, p>2p1, its initial value u(x,0)=u0(x)∈Lq−1+1m(Ω), 3>q>1 and its boundary ...
Huashui Zhan
semanticscholar   +1 more source

Near Field Asymptotic Behavior for the Porous Medium Equation on the Half-Line

Advanced Nonlinear Studies, 2017
Kamin and Vázquez [11] proved in 1991 that solutions to the Cauchy–Dirichlet problem for the porous medium equation ut=(um)x⁢x${u_{t}=(u^{m})_{xx}}$, m>1${m>1}$, on the half-line with zero boundary data and nonnegative compactly supported integrable ...
Cortázar Carmen, Quirós Fernando, Wolanski Noemi   +2 more
doaj   +1 more source

Hypocoercivity [PDF]

arXiv, 2006
This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, by means of well-chosen Lyapunov functionals. Typical examples are the kinetic Fokker--Planck and Boltzmann equation. Many open problems and possible directions for future research are discussed.
arxiv  

On a class of fully nonlinear parabolic equations

Advances in Nonlinear Analysis, 2016
We study the homogeneous Dirichlet problem for the fully nonlinear ...
Antontsev Stanislav, Shmarev Sergey
doaj   +1 more source

Inverse source problems for degenerate time-fractional PDE

, 2020
In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one involves a time ...
Al-Salti, Nasser, Karimov, Erkinjon
core