Related papers: Heat equation with singular thermal conductivity
For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation…
In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with H\"older diffusion and unbounded singular drifts in Kato's class. Moreover, we also establish sharp two-sided…
We derive the heat equation for the thermal energy under diffusive space-time scaling for a purely deterministic microscopic dynamics satisfying Newton equations perturbed by an external chaotic force acting like a magnetic field.
In this work, we introduce a notion of dissipative weak solution for a system describing the evolution of a heat-conducting incompressible non-Newtonian fluid. This concept of solution is based on the balance of entropy instead of the…
In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
In this paper, we study the temperature distribution of a body when the heat is transmitted only by radiation. The heat transmitted by convection and conduction is ignored. We consider the stationary radiative transfer equation in the local…
In the present study it is shown that the interaction of a quasi-static gravitational wave through density fluctuations gives rise to a heat conductivity coefficient and hence temperature. This fact is a very important characteristics to…
We calculate the electronic contribution to the thermal conductance in a quantum dot that is weakly coupled via tunnel barriers to two electrons reservoirs. A linear response model is derived for the calculation of the heat current Q…
This paper analyzes a transient thermo-electromagnetic problem arising in the modeling of induction heating processes. Unlike previous studies that focused on steady-state scenarios, we consider a time-dependent thermal problem coupled with…
We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bounded from below by a positive constant and the case of…
We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces.…
We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the…
We establish a unique continuation property for stochastic heat equations evolving in a bounded domain $G$. Our result shows that the value of the solution can be determined uniquely by means of its value on an arbitrary open subdomain of…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size $L$ is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_{h}$ and…
We investigate the heat flow between different terminals in an interacting coherent conductor when inelastic scattering is present. We illustrate our theory with a two-terminal quantum dot setup. Two types of heat asymmetries are…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
In this paper, we investigate stochastic heat equation with sublinear diffusion coefficients. By assuming certain concavity of the diffusion coefficient, we establish non-trivial moment upper bounds and almost sure spatial asymptotic…
A stochastic heat equation on $[0,T]\times{\mathbb{R}}$ driven by a general stochastic measure $d\mu(t)$ is investigated in this paper. For the integrator $\mu$, we assume the $\sigma$-additivity in probability only. The existence,…