Monica De Angelis

Existence, uniqueness and a priori estimates for a nonlinear integro-differential equation

The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem in all of the space is analyzed together with continuous dependence and a priori estimates of the solution. These estimates show that the asymptotic behavior is determined by the reaction mechanism. Moreover it’s possible a rigorous singular perturbation analysis for discussing travelling waves with their characteristic times.

Diffusion and wave behaviour in linear Voigt model

Abstract A boundary value problem P e related to a third order parabolic equation with a small parameter e is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases, superconducting materials, incompressible and electrically conducting fluids. Moreover, the third order parabolic operator regularizes various nonlinear second order wave equations. In this paper, the hyperbolic and parabolic behaviour of the solution of P e is estimated by means of slow time τ=et and fast time θ=t/e. As consequence, a rigorous asymptotic approximation for the solution of P e is established. To cite this article: M. De Angelis, P. Renno, C. R. Mecanique 330 (2002) 21–26

A wave equation perturbed by viscous terms: fast and slow times diffusion effects in a Neumann problem

A Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient

Asymptotic effects of boundary perturbations in excitable systems

\varepsilon

Mathematical Contributions to the Dynamics of the Josephson Junctions: State of the Art and Open Problems

ε, is investigated. Results obtained prove that for slow time

On diffusion effects of the perturbed sine-Gordon equation with Neumann boundary conditions

\varepsilon t <1