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The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
Based on a combination of insights afforded by Rainer Picard and Serge Nicaise, we extend a set of abstract piezo-electromagnetic impedance boundary conditions. We achieve this by accommodating for the influence of heat with the inclusion…
We consider a two-phase elliptic-parabolic moving boundary problem modelling an evaporation front in a porous medium. Our main result is a proof of short-time existence and uniqueness of strong solutions to the corresponding nonlinear…
We consider a second-order nonlocal parabolic MEMS equation with Dirichlet boundary conditions: \[ u_t-\Delta u=\frac{\lambda}{(1-u)^2\bigl(1+\int_\Omega\frac{1}{1-u}\,dx\bigr)^2},\quad x\in\Omega,\ t>0, \] where…
Motivated by a long-standing debate concerning the nature and interrelations of surface-tension variables in fluid membranes, we reformulate the thermodynamics of a membrane vesicle as a generic two-dimensional finite system enclosing a…
An $\mathrm{L}_1$-maximal regularity theory for parabolic evolution equations inspired by the pioneering work of Da Prato and Grisvard is developed. Besides of its own interest, the approach yields a framework allowing global-in-time…
We cope with a free boundary fluid-structure interaction model. In the model, the viscous incompressible fluid interacts with elastic body via the common boundary. The motion of the fluid is governed by Navier-Stokes equations while the…
We study the asymptotics for large time of solutions to a one dimensional parabolic evolution equation with non-standard measure-valued right hand side, that involves derivatives of the solution computed at a free boundary point. The…
The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the…
When a (frequency-domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the…
Consider an ambient medium and a heterogeneous entity composed of a bidimensional material surrounded by a thin membrane. The electromagnetic constants of these materials are different. By analogy with biological cells, we call this entity…
Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries…
Thermal Energy Storage (TES) devices, which leverage the constant-temperature thermal capacity of the latent heat of a Phase Change Material (PCM), provide benefits to a variety of thermal management systems by decoupling the absorption and…
This paper describes an embedded boundary (EB) approach for simulating three-dimensional fluid flow on a staggered mesh where the velocity components are defined on cell faces and the thermodynamic state is defined on cell centers. Most EB…
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode…
In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on…
This paper is concerned with the existence and uniqueness of the solution to a doubly nonlinear parabolic problem which arises directly from a circuit model of microwave heating. Beyond the relevance from a physical point of view, the…
We derive and implement a suitable boundary condition for the kinetic description of the electrons inside a plasma, which takes into account microphysical processes inside the wall. It is based on the surface scattering kernel, which…
An excitation method for MEMS devices with planar electrodes is described. The stationary part of the device (the stator) consists of three electrode arrays arranged in the 'ABCABC' order. 'A', 'B', and 'C' carry time-independent potentials…
This paper studies asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with two species of cells: proliferating cells and quiecent cells. In previous literatures it has been proved that this problem has…