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For a wave equation with pure delay, we study an inhomogeneous initial-boundary value problem in a bounded 1D domain. Under smoothness assumptions, we prove unique existence of classical solutions for any given finite time horizon and give…

Here, the perturbation equation for a dissipative medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes's hypothesis. The dispersion relations of this generic governing equation…

We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models…

We discuss the general conditions ensuring relativistic causality in an effective theory based on the derivative expansion. Relativistic causality implies that the Green function vanishes in the space-like region. It is known that a naive…

Observations and theory suggest that line driven winds from hot stars and luminous accretion disks adopt a unique, critical solution which corresponds to maximum mass loss rate. We analyze the numerical stability of the infinite family of…

The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…

An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…

Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discon- tinuous derivative can generate multiple…

We consider the damped hyperbolic equation in one space dimension $\epsilon u_{tt} + u_t = u_{xx} + F(u)$, where $\epsilon$ is a positive, not necessarily small parameter. We assume that $F(0)=F(1)=0$ and that $F$ is concave on the interval…

We investigate the long time behaviour of the $L^2$-energy of solutions to wave equations with variable speed. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation…

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of [Evers, Hille and Muntean.…

We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial…

Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we…

We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…

We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any…

We study a porous medium equation with fractional potential pressure: $$ \partial_t u= \nabla \cdot (u^{m-1} \nabla p), \quad p=(-\Delta)^{-s}u, $$ for $m>1$, $0<s<1$ and $u(x,t)\ge 0$. The problem is posed for $x\in \mathbb{R}^N$, $N\geq…

We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…

In the first part of this paper, we show that the Cauchy problem for wave propagation in some static spacetimes presenting a singular time-like boundary is well posed, if we only demand the waves to have finite energy, although no boundary…

Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…

We study several basic dispersive models with random periodic initial data such that the different Fourier modes are independent random variables. Motivated by the vast Physics literature on related topics, we then study how much the…