Related papers: The bidomain problem as a gradient system
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
In the framework of bidifferential graded algebras, we present universal solution generating techniques for a wide class of integrable systems.
We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
In this paper we study the conditions for the existence of strong solutions (both local and global) for stochastic bidomain equations. To this end, we use apriori energy estimates and Serrin-type theorems. We further address the asymptotic…
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion…
In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
Smart grid technological advances present a recent class of complex interdisciplinary modeling and increasingly difficult simulation problems to solve using traditional computational methods. To simulate a smart grid requires a systemic…
In this paper, we study the existence of positive entire large and bounded radial positive solutions for a nonlinear system. Our results give an answer of the question raised in [11].
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
The aim of this note is two-fold. In the first part of the paper we are going to investigate an inverse problem related to additive energy. In the second, we investigate how dense a subset of a finite structure can be for a given additive…
Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include phase transitions of…
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space…
We consider the $k$-dispersion generalized Benjamin-Ono equation in the supercritical case. We establish sharp conditions on the data to show global well-posedness in the energy space for this family of nonlinear dispersive equations. We…
Existence, regularity and location of solutions to quasilinear singular elliptic systems with general gradient dependence are established developing a method of sub-supersolution. The abstract theorems involving sub-supersolutions are…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
Networked systems are systems of interconnected components, in which the dynamics of each component are influenced by the behavior of neighboring components. Examples of networked systems include biological networks, critical…
This lecture note focuses on comparing the notions of invariance and home spaces in Transition Systems and more particularly, in Petri Nets. We also describe how linear algebra relates to these basic notions in Computer Science, how it can…