Zobrazeno 1 - 10
of 1 181
pro vyhledávání: '"35B30"'
Autor:
Tsopanopoulos, Michael
The model problem of a plane angle for a second-order elliptic system with Dirichlet, mixed, and Neumann boundary conditions is analyzed. The existence of solutions of the form $r^\lambda v$ is, for each boundary condition, reduced to solving a matri
Externí odkaz:
http://arxiv.org/abs/2412.11858
Autor:
Shao, Kerun
We study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and $\partial^{\leq\kappa}F(0)
Externí odkaz:
http://arxiv.org/abs/2412.05544
We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the problem, we produ
Externí odkaz:
http://arxiv.org/abs/2411.15335
Autor:
Goldys, Ben, Peszat, Szymon
Let $P_s\phi(x)=\mathbb{E}\, \phi(X^x(s))$, be the transition semigroup on the space $B_b(E)$ of bounded measurable functions on a Banach space $E$, of the Markov family defined by the linear equation with additive noise $$ d X(s)= \left(AX(s) + a\ri
Externí odkaz:
http://arxiv.org/abs/2410.20074
Autor:
Magaña, Marc
We prove that the solution map for a family of non-linear transport equations in $\mathbb{R}^n$, with a velocity field given by the convolution of the density with a kernel that is smooth away from the origin and homogeneous of degree $-(n-1)$, is co
Externí odkaz:
http://arxiv.org/abs/2410.19057
In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in $\mathbb{R}^N$. Different homogeneous boundary conditions are considered, includi
Externí odkaz:
http://arxiv.org/abs/2410.13335
Autor:
Nguyen, Hoai-Minh
We construct a static feedback control in a trajectory sense and a dynamic feedback control to obtain the local rapid boundary stabilization of a KdV system using Gramian operators. We also construct a time-varying feedback control in the trajectory
Externí odkaz:
http://arxiv.org/abs/2409.11768
Autor:
Krupa, Sam G., Székelyhidi Jr, László
We develop a general framework for studying non-uniqueness of the Riemann problem for the isentropic compressible Euler system in two spatial dimensions, and in this paper we present the most delicate result of our method: non-uniqueness of the conta
Externí odkaz:
http://arxiv.org/abs/2409.11296
This work considers the Fr\'echet derivative of the idealized forward map of two-dimensional electrical impedance tomography, i.e., the linear operator that maps a perturbation of the coefficient in the conductivity equation over a bounded two-dimens
Externí odkaz:
http://arxiv.org/abs/2409.10671
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an open inter
Externí odkaz:
http://arxiv.org/abs/2408.16435