Results 101 to 110 of about 1,990 (139)

Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]

Calc Var Partial Differ Equ, 2021
Bögelein V, Heran A, Schätzler L, Singer T.   +3 more
europepmc   +1 more source

Sharp Harnack inequalities for a family of hypoelliptic diffusions [PDF]

arXiv, 2015
We prove sharp Harnack inequalities for a family of Kolmogorov-Fokker-Planck type hypoelliptic diffusions.
arxiv  

On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient

Electronic Journal of Differential Equations, 2002
We study the Cauchy problem for the nonlinear (possibly strongly) degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(x)f(u))=partial_x^2 A(u), quad A'(cdot)ge 0, $$ where the coefficient $gamma(x)$ is possibly ...
John D. Towers, Nils H. Risebro, Kenneth H. Karlsen   +2 more
doaj  

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 degenerate migration-consumption model in domains of arbitrary dimension

Advanced Nonlinear Studies
In a smoothly bounded convex domain Ω⊂Rn ${\Omega}\subset {\mathbb{R}}^{n}$ with n ≥ 1, a no-flux initial-boundary value problem forut=Δuϕ(v),vt=Δv−uv, $$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv ...
Winkler Michael
doaj   +1 more source

Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity

, 2014
In this paper, we establish a local gradient estimate for a $p$-Lpalacian equation with a fast growing gradient nonlinearity. With this estimate, we can prove a parabolic Liouville theorem for ancient solutions satisfying some growth restriction near ...
Attouchi, Amal
core   +1 more source

Decay of periodic entropy solutions to degenerate nonlinear parabolic equations [PDF]

arXiv, 2019
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
arxiv  

On a nonlinear compactness lemma in L^p(0,T;B) [PDF]

arXiv, 2001
We consider a nonlinear counterpart of a compactness lemma of J. Simon, which arises naturally in the study of doubly nonlinear equations of elliptic-parabolic type. Our work was motivated by previous results J. Simon, recently sharpened by H. Amann, in the linear setting, and by a nonlinear compactness argument of H.W. Alt and S. Luckhaus.
arxiv  

Critical heat kernel estimates via Hardy-Sobolev inequalities [PDF]

arXiv, 2003
We obtain Sobolev inequalities for the Schrodinger operator -\Delta-V, where V has critical behaviour V(x)=((N-2)/2)^2|x|^{-2} near the origin. We apply these inequalities to obtain pointwise estimates on the associated heat kernel, improving upon earlier results.
arxiv  

Existence of solutions to a diffusive shallow medium equation. [PDF]

J Evol Equ, 2021
Bögelein V, Dietrich N, Vestberg M.
europepmc   +1 more source