Related papers: A dyadic model on a tree
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
In this article we consider a class of state-dependent delay differential equations which is modelling the dynamics of the number of adult trees in forests. We prove the boundedness of solutions for a single species model as well as a…
Physics-based simulations typically operate with a combination of complex differentiable equations and many scientific and geometric inputs. Our work involves gathering data from those simulations and seeing how well tree-based machine…
In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
In this paper we study the linear wave equation on an $n$-dimensional spatial domain. We show that there is a boundary triplet associated to the undamped wave equation. This enables us to characterise all boundary conditions for which the…
We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
A novel model of wave turbulence is presented which allows to explain in the same frame various nonlinear wave phenomena: intermittency, form and direction of the energy cascades, formation of a zero-frequency band with non-zero energy,…
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…
We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a…
We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up…
Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) full von Karman shallow shell equations that accounts for both…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
We investigate a system of nonlinear partial differential equations modeling the unsteady flow of a shear-thinning non-Newtonian fluid with a concentration-dependent power-law index. The system consists of the generalized Navier-Stokes…
Within the Large Eddy Simulation framework, we propose a methodology based on the Lie theory to derive symmetry-preserving turbulence models. We apply this methodology to the incompressible Navier-Stokes equations.} These models explicitly…
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier…
In this paper, we prove the global existence of strong solutions for the 3D incompressible inhomogeneous viscoelastic system. We do not assume the "initial state" assumption and the "div-curl" structure inspired by the works [59,61]. It is…