Related papers: Some results on evolution

Let $X$ be a negatively curved symmetric space and $\Gamma$ a non-cocompact lattice in $\rm{Isom}(X)$. We show that small, parabolic-preserving deformations of $\Gamma$ into the isometry group of any negatively curved symmetric space…

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the $C^0$-topological context, and provide necessary and sufficient regularity conditions for the (standard) $C^k$-topological setting. We prove that the…

We consider the Cauchy problem $(\mathbb D_{(k)} u)(t)=\lambda u(t)$, $u(0)=1$, where $\mathbb D_{(k)}$ is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory {\bf 71} (2011),…

Let M be a connected real-analytic hypersurface in N-dimensional complex euclidean space whose Levi form is nondegenerate at some point. We prove that for every point p in M, there exists an integer k=k(M,p) such that germs at p of local…

The aim of this paper is to state and prove existence and uniqueness results for a general elliptic problem with homogeneous Neumann boundary conditions, often associated with image processing tasks like denoising. The novelty is that we…

Let $\Omega\subset\mathbb{R}^{d}$ be an open set. Given a boundary datum $g$ on $\partial\Omega$ and a function $K:\bar {\Omega} \to\mathcal{K}$, the family of all compact convex subsets of $\mathbb{R}^{d}$, we prove the existence of…

Let E be an arbitrary graph, K be any field and let L be the corresponding Leavitt path algebra. Necessary and sufficient conditions (which are both algebraic and graphical) are given under which all the irreducible representations of L are…

Evolution algebras are a special class of non-associative algebras exhibiting connections with different fields of Mathematics. Hilbert evolution algebras generalize the concept through a framework of Hilbert spaces. This allows to deal…

A kinetic equation for the collisional evolution of stable, bound, self gravitating and slowly relaxing systems is established, which is valid when the number of constituents is very large. It accounts for the detailed dynamics and self…

We present a general method of solving the Cauchy problem for multidimensional parabolic (diffusion type) equation with variable coefficients which depend on spatial variable but do not change over time. We assume the existence of the…

In this paper we show that evolution algebras over any given field $\Bbbk$ are universally finite. In other words, given any finite group $G$, there exist infinitely many regular evolution algebras $X$ such that $Aut(X)\cong G$. The proof…

This survey reports on current progress of programs to classify graph C*-algebras and Leavitt path algebras up to Morita equivalence using K-theory. Beginning with an overview and some history, we trace the development of the classification…

The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for $H^s$ initial data, $s>-1/2$, and for any $s_1<\min(3s+1,s+1)$, the difference of the nonlinear and linear evolutions is in $H^{s_1}$…

In this paper, we consider the following general evolution equation $$ u_t=\Delta_fu+au\log^\alpha u+bu $$ on smooth metric measure spaces $(M^n, g, e^{-f}dv)$. We give a local gradient estimate of Souplet-Zhang type for positive smooth…

In this article we deal with the stability and convergence of numerical solutions of nonlinear evolution equations of the form $A(u(t))+f(u(t))=u'(t)$, the numerical analysis of solutions to this problems will be performed using some…

In this paper, we consider the following nonlinear elliptic equation with Dirichlet boundary condition: $-\Delta u=K(x)u^{\frac{n+2}{n-2}},\, u>0$ in $\Omega,\, u=0$ on $\partial\Omega$, where $\Omega$ is a smooth bounded domain in…

A colouring of a graph $G=(V,E)$ is a mapping $c\colon V\to \{1,2,\ldots\}$ such that $c(u)\neq c(v)$ for every two adjacent vertices $u$ and $v$ of $G$. The {\sc List $k$-Colouring} problem is to decide whether a graph $G=(V,E)$ with a…

The problem of characterizing GKLS-generators and CP-maps with an invariant appeared in different guises in the literature. We prove two unifying results which hold even for weakly closed *-algebras: First, we show how to construct a normal…

Given a closed surface $S$ with finitely generated Veech group $G$ and its $\pi_1(S)$-extension $\Gamma$, there exists a hyperbolic space $\hat{E}$ on which $\Gamma$ acts isometrically and cocompactly. The space $\hat{E}$ is obtained by…

In this paper we deal with an inhomogeneous parabolic Dirichlet problem involving the 1-Laplacian operator. We show the existence of a unique solution when data belong to $L^1(0,T;L^2(\Omega))$ for every $T>0$. As a consequence, global…