相关论文: Coleman-Gurtin type equations with dynamic boundar…

We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed.…

The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and…

Motivated by diffusion processes on metric graphs and ramified spaces, we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class. Beside well-posedness, we discuss…

We consider the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic…

We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…

This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…

The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…

The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…

This article is intended to present a qualitative and numerical analysis of well-posedness and boundary stabilization problems of the well-known Korteweg-de Vries-Burgers equation. Assuming that the boundary control is of memory type, the…

In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behavior of automated vehicles. The properties of the solutions of this equation are studied by introducing the appropriate notion of a weak…

Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for…

We study various formulations of the boundary conditions for the Euler equations of gas dynamics from a mathematical and numerical point of view. In the case of one space dimension, we recall the classical results, based on an analysis of…

We prove a general inequality between the charge current and its fluctuations valid for any non-interacting coherent electronic conductor and for any stationary out-of-equilibrium condition, thereby going beyond established…

The sine-Gordon equation exhibits a gap in its linear spectrum. That gives rise to memory, or non-Markovian, effects in the soliton formation processes. The generalized variational approach is suggested to derive the model equation that…

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

The Kramers problem for quantum Bose-gases with specular-diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers' problem the new generalized method of a source of the decision of the boundary problems from…

In the framework of the Lagrangian field theory, we derive a type of new non-classical natural boundary condition to be correlated with the mean curvature of boundary surface. Under the condition of homogeneity and isotropy, this type of…

We find the spectrum of boundary bound states for the sine-Gordon model with Dirichlet boundary conditions, closing the bootstrap and providing a complete description of all the poles in the boundary reflection factors. The boundary…

Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…

We show existence of a non-equilibrium steady state for the one-dimensional, non-linear BGK model on an interval with diffusive boundary conditions. These boundary conditions represent the coupling of the system with two heat reservoirs at…