Results 41 to 50 of about 389 (66)

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  

Relativistic stable operators with critical potentials [PDF]

arXiv, 2022
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.
arxiv  

Initial value problems for diffusion equations with singular potential [PDF]

, 2012
Let $V$ be a nonnegative locally bounded function defined in $Q_\infty:=\BBR^n\times(0,\infty)$. We study under what conditions on $V$ and on a Radon measure $\gm$ in $\mathbb{R}^d$ does it exist a function which satisfies $\partial_t u-\xD u+ Vu=0$ in ...
Gkikas, Konstantinos, Veron, Laurent
core   +2 more sources

Regularity and long time behavior of a doubly nonlinear parabolic problem and its discretization

, 2023
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations obtained by a finite
Egger, Herbert, Giesselmann, Jan
core  

On fractional parabolic equations with Hardy-type potentials [PDF]

arXiv, 2022
A classification of local asymptotic profiles and strong unique continuation properties are established for a class of fractional heat equations with a Hardy-type potential, via an Almgren-Poon monotonicity formula combined with a blow-up analysis.
arxiv  

A critical non-homogeneous heat equation with weighted source

European Journal of Applied Mathematics
Some qualitative properties of radially symmetric solutions to the non-homogeneous heat equation with critical density and weighted source \begin{align*} |x|^{-2}\partial _tu=\Delta u+|x|^{\sigma }u^p, \quad (x,t)\in {\mathbb {R}}^N\times (0,T), \end ...
Razvan Gabriel Iagar, Ariel Sánchez
doaj   +1 more source

Total variation denoising in $l^1$ anisotropy

, 2017
We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional.
Berkels B., Hochbaum D. S., Michał Łasica, Mucha P. B., Piotr B. Mucha, Salvador Moll   +5 more
core   +1 more source

On parabolic equations with critical electromagnetic potentials [PDF]

arXiv, 2018
We consider a class of parabolic equations with critical electromagnetic potentials, for which we obtain a classification of local asymptotics, unique continuation results, and an integral representation formula for solutions.
arxiv  

On parabolic equations in Morrey spaces with VMO $a$ and Morrey $b,c$ [PDF]

arXiv, 2023
We prove existence and uniqueness of solutions in Morrey spaces of functions with mixed norms for second-oder parabolic equations in the whole space with VMO $a$ and Morrey $b,c$.
arxiv  

Classification of local asymptotics for solutions to heat equations with inverse-square potentials [PDF]

arXiv, 2010
Asymptotic behavior of solutions to heat equations with spatially singular inverse-square potentials is studied. By combining a parabolic Almgren type monotonicity formula with blow-up methods, we evaluate the exact behavior near the singularity of solutions to linear and subcritical semilinear parabolic equations with Hardy type potentials.
arxiv