Related papers: An Inverse Stefan Problem Relevant to Boilover: He…
Two Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order $ \al \in (0,1) $ is taken in the Caputo's sense. The first one has a constant condition on $ x = 0 $ and the second presents a…
Israel-Stewart theory is a causal, stable formulation of relativistic dissipative fluid dynamics. This theory has been shown to give a decent description of the dynamical behavior of a relativistic fluid in cases where shear stress becomes…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium…
The classical Stefan problem is reduced as the singular limit of phase-field equations. These equations are for temperature $u$ and the phase-field $\varphi$, consists of a heat equation: $$ u_t+\ell\varphi_t=\Delta u, $$ and a…
Internally heated convection involves the transfer of heat by fluid motion between a distribution of sources and sinks. Focusing on the balanced case where the total heat added by the sources matches the heat taken away by the sinks, we…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
In this paper, the dynamics of an incompressible fluid in a bounded connected domain, described by Navier-Stokes equations coupled with a heat transfer equation, is investigated by a method inspired from the non-commutative strategy…
We derive two weak formulations for the supercooled Stefan problem with transport noise on a half-line: one captures a continuously evolving system, while the other resolves blow-ups by allowing for jump discontinuities in the evolution of…
This work is aimed at the study and analysis of the heat transport on a metal bar of length $L$ with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials.…
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by…
We consider a steady-state heat conduction problem in a multidimensional bounded domain Omega for the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion Gamma_1 of…
In this paper a 3-phase Stefan problem solution method for 1D semi-infinity alloy is developed. The problem is first solved for full enthalpy of the system and then the thermal diffusivity has been eliminated from the divergence operator by…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
A new two-layer model has been proposed to study microscale heat transfer associated with a developing flow boundary layer. As an example, a cold, microscale film of liquid impinging on an isothermal hot, horizontal surface has been…
In this paper a one-phase Stefan problem with size-dependent thermal conductivity is analysed. Approximate solutions to the problem are found via perturbation and numerical methods, and compared to the Neumann solution for the equivalent…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…