相关论文: Initial behavior of solutions to the Yang-Mills he…

We discuss the unique solvability of the third initial-boundary value problem for the heat equation in a bounded domain. This problem has uniquely a time-global solution in the anisotropic Sobolev space $W^{2,1}_{p,q}$ for any $1<p<\infty$,…

We study the large time behavior of solutions to a non-local diffusion equation, $u_t=J*u-u$ with $J$ smooth, radially symmetric and compactly supported, posed in $\mathbb{R}_+$ with zero Dirichlet boundary conditions. In sets of the form…

In this manuscript we consider a non-local porous medium equation with non-local diffusion effects given by a fractional heat operator \begin{equation*} \partial_t u = \mbox{div}(u\nabla p),\qquad \partial_t p = -(-\Delta)^s p + u^2,…

We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to $a=0.015$ fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of…

Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal curvature flow for convex closed plane curves and discuss the short time existence and asymptotic convergence behavior of the flow. Due to the linear structure…

This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with K\"ahler metrics $\omega_\epsilon$…

We investigate the time-asymptotic properties of solutions of the differential equation x''(t) + a(t)x'(t) + g(x(t)) = 0 in a Hilbert space, where a(.) is non-increasing and g is the gradient of a potential G. If the coefficient a(.) is…

There are several models for heat conduction - non-Fourier equations - in the literature that are important for various practical problems. These models manifest themselves in partial differential equations, and the application of which…

We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the…

In this paper, we shall prove that, on a non-flat Riemannian vector bundle over a compact Riemannian manifold, the smooth solution of the Yang-Mills flow will blow up in finite time if the energy of the initial connection is small enough.…

In this paper, we consider the initial boundary value problem for the three-dimensional viscous primitive equations of large-scale moist atmosphere which are used to describe the turbulent behavior of long-term weather prediction and…

We prove global well-posedness of the $ 3d $ Yang-Mills equation in the temporal gauge in $ H^{\sigma} $ for $ \sigma > \frac{5}{6} $. Unlike related equations, Yang-Mills is not directly amenable to the method of almost conservation laws…

We consider the solution of $u_t-\Delta^G_p u=0$ in a (not necessarily bounded) domain, satisfying $u=0$ initially and $u=1$ on the boundary at all times. Here, $\Delta^G_p u$ is the game-theoretic or normalized $p$-laplacian. We derive new…

In this paper, the initial and boundary problem of the difference equation which is a discretization of the semi-linear heat equation. The difference equation derived by discretizing the semi-linear heat equation has solutions which show…

The equation of state of $SU(3)$ Yang-Mills theory is investigated in the framework of a moving reference frame. Results for the entropy density, the pressure, the energy density, and the trace anomaly are presented for temperatures ranging…

We study the late-time behavior of spherically symmetric solutions of the Yang-Mills equations on Minkowski and Schwarzschild backgrounds. Using nonlinear perturbation theory we show in both cases that solutions having smooth compactly…

We study the behaviour of nonnegative solutions to the quasilinear heat equation with a reaction localized in a ball $$ u_t=\Delta u^m+a(x)u^p, $$ for $m>0$, $0<p\le\max\{1,m\}$, $a(x)=\mathds{1}_{B_L}(x)$, $0<L<\infty$ and $N\ge2$. We…

The large time behavior of zero mass solutions to the Cauchy problem for a convection-diffusion equation. We provide conditions on the size and shape of the initial datum such that the large time asymptotics of solutions is given either by…

We study higher dimensional quartic quasi-topological black holes in the framework of non-abelian power-Yang-Mills theory. It is shown that real solutions of the gravitational field equations exist only for positive values of quartic…

In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…