A mixed problem with only integral boundary conditions for a hyperbolic equation.
A mixed semilinear parabolic problem from combustion theory.
A mixed-culture model of a probiotic biofilm control system.
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the...
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the...
A mixed-Lagrange multiplier finite element method for the polyharmonic equation
A model for dip-coating of a two liquid mixture.
A model for passive damping of a membrane
A model for phenomena of instability
A model for Toepliz operators in the space of entire functions of exponential type
A model of a radially symmetric cloud of self-attracting particles
We consider a parabolic equation which describes the gravitational interaction of particles. Existence of solutions and their convergence to stationary states are studied.
A model of atomic radiation
A model of evolution of temperature and density of ions in an electrolyte
We study existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions. In this model the evolution of temperature is also taken into account. For stationary states the existence of an external potential is also assumed.
A model of frontal polymerization including the gel effect.
A model of frontal polymerization using complex initiation.
A model problem for boundary layers of thin elastic shells
We consider a model problem (with constant coefficients and simplified geometry) for the boundary layer phenomena which appear in thin shell theory as the relative thickness ε of the shell tends to zero. For ε = 0 our problem is parabolic, then it is a model of developpable surfaces. Boundary layers along and across the characteristic have very different structure. It also appears internal layers associated with propagations of singularities along the characteristics. The special structure of...
A modern proof of the Maximum Principle
A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems.
A modified quasi-boundary value method for the backward time-fractional diffusion problem
In this paper, we consider a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine the initial data from a noisy final data. Based on a series expression of the solution, a conditional stability for the initial data is given. Further, we propose a modified quasi-boundary value regularization method to deal with the backward problem and obtain two kinds of convergence rates by using an a priori regularization parameter...
A monotonicity method for solving hyperbolic problems with hysteresis