On the hyperbolic Dirichlet to Neumann functional.
On the limit amplitude principle for a layer.
On the non-convergence of successive approximations in the Darboux problem for the equation
On the nonlinear stabilization of the wave equation
We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.
On the Picard problem for hyperbolic differential equations in Banach spaces
B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].
On the problem of determining the parameters of a layered elastic medium and an impulse source.
On the problem of determining the structure of a layered medium and the shape of an impulse source.
On the quenching of solutions of the wave equation with a nonlinear boundary condition.
On the regularity of boundary traces for the wave equation
On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
On the singularities of 3-D Protter's problem for the wave equation.
On the solvability of a Darboux type non-characteristic spatial problem for the wave equation.
On the solvability of a multidimensional version of the Goursat problem for a second order hyperbolic equation with characteristic degeneration.
On the solvability of a spatial problem of Darboux type for the wave equation.
On the solvability of parabolic and hyperbolic problems with a boundary integral condition.
On the solvability of the multidimensional version of the first Darboux problem for a model second-order degenerating hyperbolic equation.
On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the...
On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type
On the wave equations with memory in noncylindrical domains.
On the well-posedness and regularity of the wave equation with variable coefficients
An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.