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 regularity properties of non-linear wave equations
On the relation of delay equations to first-order hyperbolic partial differential equations
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a single first-order hyperbolic partial differential equation under the effect of measurable inputs acting on...
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 sign of Colombeau functions and applications to conservation laws
A generalized concept of sign is introduced in the context of Colombeau algebras. It extends the sign of the point-value in the case of sufficiently regular functions. This concept of generalized sign is then used to characterize the entropy condition for discontinuous solutions of scalar conservation laws.
On the singularities of 3-D Protter's problem for the wave equation.
On the solution -dimensional of the product operator and diamond Bessel operator.
On the solution of the nonlinear wave equation by the decomposition method.
On the solution of transonic flows with weak shocks
On the solution sets of some nonconvex hyperbolic differential inclusions
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 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.