Zobrazeno 1 - 10
of 420
pro vyhledávání: '"35K67"'
Autor:
Elliott, Charles M., Sales, Thomas
In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward Euler time di
Externí odkaz:
http://arxiv.org/abs/2411.05650
Autor:
Bravin, Marco, Gnann, Manuel V., Knüpfer, Hans, Masmoudi, Nader, Roodenburg, Floris B., Sauer, Jonas
Well-posedness and higher regularity of the heat equation with Robin boundary conditions in an unbounded two-dimensional wedge is established in an $L^{2}$-setting of monomially weighted spaces. A mathematical framework is developed which allows to o
Externí odkaz:
http://arxiv.org/abs/2411.04651
Autor:
Bekmaganbetov, Bekarys, Dong, Hongjie
We investigate the inhomogeneous boundary value problem for elliptic and parabolic equations in divergence form in the half space $\{x_d > 0\}$, where the coefficients are measurable, singular or degenerate, and depend only on $x_d$. The boundary dat
Externí odkaz:
http://arxiv.org/abs/2410.08293
Autor:
Hivert, Hélène, Salin, Florian
In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion equation by inc
Externí odkaz:
http://arxiv.org/abs/2409.18629
Autor:
Metafune, Giorgio, Sobajima, Motohiro
We characterize the domain of the Schr\"odinger operators $S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0<\alpha<2$ and $c\in\mathbb{R}$. When $\alpha p< N$, the domain characterization is essentially known and can be proved using differen
Externí odkaz:
http://arxiv.org/abs/2409.09917
This paper studies a class of linear parabolic equations in non-divergence form in which the leading coefficients are measurable and they can be singular or degenerate as a weight belonging to the $A_{1+\frac{1}{n}}$ class of Muckenhoupt weights. Kry
Externí odkaz:
http://arxiv.org/abs/2409.09437
Autor:
Jüngel, Ansgar, Li, Yue
A spectral-fractional Cahn-Hilliard cross-diffusion system, which describes the pre-patterning of lymphatic vessel morphology in collagen gels, is studied. The model consists of two higher-order quasilinear parabolic equations and describes the evolu
Externí odkaz:
http://arxiv.org/abs/2408.05972
Autor:
Negro, Luigi, Spina, Chiara
We prove sharp upper and lower estimates for the parabolic kernel of the singular elliptic operator \begin{align*} \mathcal L&=\mbox{Tr }\left(AD^2\right)+\frac{\left(v,\nabla\right)}y, \end{align*} in the half-space $\mathbb{R}^{N+1}_+=\{(x,y): x \i
Externí odkaz:
http://arxiv.org/abs/2408.00031
Autor:
Arora, Rakesh, Shmarev, Sergey
We study how the smoothness of the initial datum and the free term affect the global regularity properties of solutions to the Dirichlet problem for the class of parabolic equations of $p(x,t)$-Laplace type %with nonlinear sources depending on the so
Externí odkaz:
http://arxiv.org/abs/2407.20133
Autor:
Bäuerlein, Fabian
We consider vector valued weak solutions $u:\Omega_T\to \mathbb{R}^N$ with $N\in \mathbb{N}$ of degenerate or singular parabolic systems of type \begin{equation*} \partial_t u - \mathrm{div} \, a(z,u,Du) = 0 \qquad\text{in}\qquad \Omega_T= \Omega\tim
Externí odkaz:
http://arxiv.org/abs/2407.17837