On the solvability of the multidimensional version of the first Darboux problem for a model second-order degenerating hyperbolic equation.
On the stability analysis of Darboux problem on both bounded and unbounded domains
In this paper, we first investigate the existence and uniqueness of solution for the Darboux problem with modified argument on both bounded and unbounded domains. Then, we derive different types of the Ulam stability for the proposed problem on these domains. Finally, we present some illustrative examples to support our results.
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 stability of the Dirichlet problem for the vibrating string equation
On the stabilization of laminated beams with delay
Of concern in this paper is the laminated beam system with frictional damping and an internal constant delay term in the transverse displacement. Under suitable assumptions on the weight of the delay, we establish that the system's energy decays exponentially in the case of equal wave speeds of propagation, and polynomially in the case of non-equal wave speeds.
On the Stabilization of the Wave Equation by the Boundary
* Partially supported by CNPq (Brazil)We study the distribution of the (complex) eigenvalues for interior boundary value problems with dissipative boundary conditions in the case of C 1 -smooth boundary under some natural assumption on the behaviour of the geodesics. As a consequence we obtain energy decay estimates of the solutions of the corresponding wave equation.
On the stabilization of wave-advection coupling. (Sur la stabilisation d'un couplage ondes-advection.)
On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws
On the strongly damped wave equation with nonlinear damping and source terms.
On the uniformly continuity of the solution map for two dimensional wave maps.
On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type
On the validity of Chapman-Enskog expansions for shock waves with small strength.
On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition
On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I : derivation of necessary conditions
On the vanishing viscosity approximation to the Cauchy problem for a 2 × 2 system of conservation laws
On the wave equation in curved spacetime
On the Wave Equation on a Compact Riemannian Manifold withour Conjugate Points.
On the wave equations with memory in noncylindrical domains.
On the weakly nonlinear wave equation involving a small parameter at the highest derivative
On the well posedness of a system of balance laws with data