Related papers: Generalized heat-transport equations: Parabolic an…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
We propose a causal heat conduction model based on a heat kernel violating the fading memory paradigm. The resulting transport equation produces an equation for the temperature. The model is applied to the discussion of two important issues…
We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…
We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the…
We obtain an analytical expression for the heat current between two overdamped quantum oscillators interacting with local thermal baths at different temperatures. The total heat current is split into classical and quantum contributions. We…
A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…
We study the ablation problem for the hyperbolic heat equation in an axisymmetrical geometry which can be conveniently realized in the lab. We determine an analytic solution which shows the approach to steady state. The thermal relaxation…
Based on the recent work [1,2], we formulate the first law and the second law of stochastic thermodynamics in the framework of general relativity. These laws are established for a charged Brownian particle moving in a heat reservoir and…
We show that the GENERIC model for relativistic heat conduction is a multifluid of Carter. This allows one to compute the multifluid constitutive relations directly from the GENERIC formalism. As a quick application, we prove that, in the…
We consider the multidimensional Euler-Poisson equations with non-zero heat conduction, which consist of a coupled hyperbolic-parabolic-elliptic system of balance laws. We make a deep analysis on the coupling effects and establish a local…
In this paper, we study a hyperbolic-parabolic coupled system arising in nonlinear three-dimensional thermoelasticity. We establish the global well-posedness and asymptotic behavior of solutions. Our main result shows that, a thermoelastic…
Present-day thermodynamics has long outgrown the initial frames of the heat-engine theory and transmuted into a rather general macroscopic method for studying kinetics of various transfer processes in their inseparable connection with the…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
We consider a class of stochastic models for energy transport and study relations between the thermal conductivity and some static observables, such as the static conductivity, which is defined as the contribution of static correlations in…
The heat-balance integral method of Goodman has been thoroughly analyzed in the case of a parabolic profile with unspecified exponent depending on the boundary condition imposed. That the classical Good man's boundary conditions defining…
We consider a one-dimensional system arising from a chemotaxis model in tumour angiogenesis, which is described by a Keller-Segel equation with singular sensitivity. This hyperbolic-parabolic system is known to allow viscous shocks…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…
We consider two hydrodynamic model problems (one incompressible and one compressible) with three dimensional fluid flow on the torus and temperature-dependent viscosity and conductivity. The ambient heat for the fluid is transported by the…