Related papers: An analytical connection between temporal and spat…
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
Many applications of contemporary science involve multiscale dynamics, which are typically characterized by the time and space scale separation of patterns of motion, with fewer slowly evolving variables and much larger set of faster…
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…
We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatio-temporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time and…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
Diffusion-induced turbulence in spatially extended oscillatory media near a supercritical Hopf bifurcation can be controlled by applying global time-delay autosynchronization. We consider the complex Ginzburg-Landau equation in the…
A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivative by continuous piecewise polynomials, which is strongly…
Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the…
This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…