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of 4 318
pro vyhledávání: '"35K65"'
Autor:
Mair, Andrew, Ptashnyk, Mariya
In this paper we consider the multiscale modelling of water transport in vegetated soil. In the microscopic model we distinguish between subdomains of soil and plant tissue, and use the Richards equation to model the water transport through each. Wat
Externí odkaz:
http://arxiv.org/abs/2411.01402
Autor:
Kogoj, Alessia E., Lanconelli, E.
Let $D\subseteq \mathbb{R}^n$, $n\geq 3$, be a bounded open set and let $x_0\in D$. Assume that the Newtonian potential of $D$ is proportional outside $D$ to the Newtonian potential of a mass concentrated at $\{x_0\}.$ Then $D$ is a Euclidean ball ce
Externí odkaz:
http://arxiv.org/abs/2411.00961
Autor:
Grube, Florian
We prove sharp two-sided estimates of the fundamental solution to the fractional Kolmogorov equation in $\mathbb{R}\times \mathbb{R}$ using Fourier methods. Additionally, we provide an explicit form of the fundamental solution in case of the square r
Externí odkaz:
http://arxiv.org/abs/2411.00687
Autor:
Elliott, Charles M., Sales, Thomas
We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function, and under
Externí odkaz:
http://arxiv.org/abs/2410.24147
Autor:
Andreucci, Daniele, Tedeev, Anatoli F.
We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, roughly speaking of the type of the exponential of a power of the distance from the origin. We assume here the
Externí odkaz:
http://arxiv.org/abs/2410.23075
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density $\rho$ with a continuous and compactly supported nonlinear mobility $\mathrm{m}(\rho)$ not necessarily concave. The velocity field is the negative grad
Externí odkaz:
http://arxiv.org/abs/2410.10040
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:
Gavioli, Chiara, Krejčí, Pavel
It is shown that the problem of moisture propagation in porous media with a nonlinear relation between the mass flux and the pressure gradient as a counterpart of the Darcy law exhibits the property of bounded speed of propagation even in the case of
Externí odkaz:
http://arxiv.org/abs/2410.06622
Autor:
Black, Tobias
We establish the H\"older continuity of bounded nonnegative weak solutions to \begin{align*} \big(\Phi^{-1}(w)\big)_t=\Delta w+\nabla\cdot\big(a(x,t)\Phi^{-1}(w)\big)+b\big(x,t,\Phi^{-1}(w)\big), \end{align*} with convex $\Phi\in C^0([0,\infty))\cap
Externí odkaz:
http://arxiv.org/abs/2410.03307
Autor:
Hilder, Bastian, Jansen, Jonas
We study the bifurcation of planar patterns and fast-moving pattern interfaces in an asymptotic long-wave model for the three-dimensional B\'enard-Marangoni problem, which is close to a Turing instability. We derive the model from the full free-bound
Externí odkaz:
http://arxiv.org/abs/2410.02708