相关论文: A note on Kazdan-Warner equation on networks
The purpose of this article is to study quasi linear parabolic partial differential equations of second order, posed on a bounded network, satisfying a nonlinear and non dynamical Neumann boundary condition at the vertices. We prove the…
The main purpose of this work is to provide an existence and uniqueness result for the solution of a linear parabolic system posed on a star-shaped network, which presents a new type of Kirchhoff's boundary transmission condition at the…
We study Kazdan-Warner equations on a connected finite graph via the method of the degree theory. Firstly, we prove that all solutions to the Kazdan-Warner equation with nonzero prescribed function are uniformly bounded and the Brouwer…
In this article, we are interested in semilinear, possibly degenerate elliptic equations posed on a general network, with nonlinear Kirchhoff-type conditions for its interior vertices and Dirichlet boundary conditions for the boundary ones.…
We concern in this paper the graph Kazdan-Warner equation \begin{equation*} \Delta f=g-he^f \end{equation*} on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the…
We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds.
Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion…
We study diffusion in a network which is governed by non-autonomous Kirchhoff conditions at the vertices of the graph. Also the diffusion coefficients may depend on time. We prove at first a result on existence and uniqueness using form…
The paper is concerned with a system of linear hyperbolic differential equations on a network coupled through general transmission conditions of Kirchhoff's type at the nodes. We discuss the reduction of such a problem to a system of…
The fundamental theory of energy networks in different energy forms is established following an in-depth analysis of the nature of energy for comprehensive energy utilization. The definition of an energy network is given. Combining the…
Continuous-time Markov chains have been successful in modelling systems across numerous fields, with currents being fundamental entities that describe the flows of energy, particles, individuals, chemical species, information, or other…
Let $G=(V,E)$ be a finite graph and $\Delta$ be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various conditions such that the Kazdan-Warner equation $\Delta u=c-he^u$ has a…
Studies on Kazdan--Warner equations on graphs have grown steadily, yet the fractional case remains insufficiently explored. Using topological degree theory, this work investigates the fractional Kazdan--Warner equation in the negative case…
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
In this note, we prove an existence result for generalized Kazdan-Warner equations on compact Riemannian manifolds by using the flow approach or the upper and lower solution method. In addition, we give a prior estimate for this type…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership…
In this paper we consider the Schr\"odinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schr\"odinger equation with…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…