We address a fluid–structure system which consists of the incompressible Navier–Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the glob...

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by...

In this paper we consider the Cauchy problem for the nonlinearly damped wave equation with nonlinear source utt −∆u + aut|ut|m−2 = bu|u|p−2, p > m. We prove that given any time T > 0, there exist always initial data with sufficiently negative initial energy, for which the solution blows up in time ≤ T. This result improves an earlier one by Todorova [11].

We consider the wave equation on a finite interval with fixed ends and nonuniform viscous damping. We prove that the spectrum of the associated damped wave operator uniquely determines an even damping. We then develop a refined asymptotic formula for the high frequencies. When the damping is even about the domain’s midpoint, terms in this expansion are Fourier coefficients for functions of the ...

Because of high pressure fluctuations in Combination Electronic Unit Pump (CEUP) system during fuel injection cycles, physical properties of diesel fuel including density, acoustic wave speed and bulk modulus also vary. These physical properties of fuel have significant importance in predicting the fuel injection behavior and its optimization. A 1D viscous damped mathematical model of wave equa...

In this paper we give an overview on some methods that are useful to solve a class of integrodi erential inverse problems. Precisely, we present some methods to solve integrodi erential inverse problems of parabolic type that are based on the theory of analytic semigroups, optimal regularity results and xed point arguments. A large class of physical models can be treated with this procedure, fo...

Abst rac t . The Crank-Nicolson scheme is widely used to solve numerically the diffusion equation, because of its good stability properties. It is, however, ill-behaved when large time-steps are used: the short wave-lengths may happen to be less damped than the long ones. A detailed analysis of this flaw is performed and an Mternative scheme is proposed, which removes this difficulty while pres...

The analysis of damping phenomena that occur in many physics and engineering problems, such as fluid dynamics, kinetic theory and semiconductors, is of particular interest. For this kind of problems, one needs accurate and stable approximate solutions even on large time intervals. These latter can be obtained reformulating time-dependent problems modeled by partial differential equations (PDEs)...

Time-dependent problems modeled by hyperbolic partial differential equations (PDEs) can be reformulated in terms of boundary integral equations (BIEs) and solved via the boundary element method (BEM). In this context, the analysis of damping phenomena that occur in many physics and engineering problems is of particular interest. Starting from a recently developed energetic space-time weak formu...