Related papers: An explicit Lyapunov function for reflection symme…
We propose the form of the Liouville action satisfying Polyakov conjecture on the accessory parameters for the hyperbolic singularities on the Riemann sphere.
Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a…
Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic…
We extend the concept of Lyapunov 1-forms for the case of diffu- sion processes to study its asymptotic behavior. We give some examples and a condition for the existence of these objects.
We improve the time decay estimates of solutions to the one-dimensional fractional diffusion equation involving the Caputo derivative. The equation is considered on the half-line. Depending on the boundary condition, we show that solutions…
This paper is concerned with model reference adaptive controller design for a class of nonlinear fractional order systems. Recent works on this topic rarely include direct methods and they are mostly based on indirect methods where the…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…
We study the behaviour of solutions of linear non-autonomous parabolic equations subject to Dirichlet or Neumann boundary conditions under perturbation of the domain. We prove that Mosco convergence of function spaces for non-autonomous…
The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…
Belavin's $\mathbb{Z}_n$-symmetric elliptic model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We find non-diagonal $K$-matrices for $n>2$ that satisfy the reflection equation (boundary Yang--Baxter…
In this paper, the high-frequency diffraction of a plane wave incident along a planar boundary turning into a smooth convex contour, so that the curvature undergoes a jump, is asymptotically analysed. An approach modifying the Fock…
We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions in domains with a particular geometry (annular type domains). We establish Lipschitz stability estimates in L^2…
This paper is devoted to the anomalous diffusion limit of kinetic equations with a fractional Fokker-Planck collision operator in a spatially bounded domain. We consider two boundary conditions at the kinetic scale: absorption and specular…
A parabolic system of three unknown functions, not expressible as gradient flows, is treated as three coupled gradient flows. For each unknown function, the minimizing movement scheme is used to construct a time-discrete approximate…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators…
We consider degenerate diffusion equations of the form $\partial_tp_t = \Delta f(p_t)$ on a bounded domain and subject to no-flux boundary conditions, for a class of nonlinearities $f$ that includes the porous medium equation. We derive for…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…