Related papers: Non-Autonomous Inertial Manifold Reduction
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
We consider boundary value problems for 1D autonomous damped and delayed semilinear wave equations of the type $$ \partial^2_t u(t,x)- a(x,\lambda)^2\partial_x^2u(t,x)= b(x,\lambda,u(t,x),u(t-\tau,x),\partial_tu(t,x),\partial_xu(t,x)), \; x…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an…
A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…
We show, using covariant Lyapunov vectors, that the chaotic solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of physical modes hyperbolically isolated from a set of residual degrees of…
We present and prove a Newton-Kantorovitch method for solving decoupled forward-backward stochastic differential equations (FBSDEs) involving smooth coefficients with uniformly bounded derivatives. As Newton's method is required a suitable…
A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…
We study dissipative translationally invariant free-fermionic theories with quadratic Liouvillians. Using a Lie-algebraic approach, we solve the Lindblad equation and find the density matrix at all times for arbitrary time dependence of the…
This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \varepsilon, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable…
A suitable notion of weak solution to infinite-dimensional rate-independent systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The key feature of such notion is that the energy dissipated at jump discontinuities…
We study the existence of nonnegative solutions for a system of impulsive differential equations subject to nonlinear, nonlocal boundary conditions. The system presents a coupling in the differential equation and in the boundary conditions.…
We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
We study the controllability of the differential Lyapunov equation under isospectral rotation of a linear gradient field. Specifically, control is effected by a symmetric time-varying gain-matrix constrained to have fixed eigenvalues; that…
In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based method of lines that allows us to split the spatial and time…
This paper discerns the invariant manifold of a class of ill-posed stochastic evolution equations driven by a nonlinear multiplicative noise. To be more precise, we establish the existence of mean-square random unstable invariant manifold…
Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…
This work continues a line of works on developing partially explicit methods for multiscale problems. In our previous works, we have considered linear multiscale problems, where the spatial heterogeneities are at subgrid level and are not…