Related papers: On local solutions to time-varying linear DAEs
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…
In this paper we exploit the umbral calculus framework to reformulate the so-called discrete Cauchy-Kovalevskaya extension in the scope of hypercomplex variables. The key idea is to consider not only formal power series representation for…
In this paper, we introduce a class of linear time-varying dynamic-algebraic equations(LTVDAE) of tractability index $\geq 2$ on arbitrary time scales. We propose a procedure for the decoupling of the considered class LTVDAE. In the paper…
We show that the previously proposed local transformations in E theory have a closing algebra if one adopts a simple constraint on the parameters of the transformations that constrains their dependence on the extended spacetime of E theory.…
Sufficient and necessary conditions are established for controllability of affine control systems where the control is constrained to a set whose convex hull contains the origin but is not necessarily, in contrast with previously known…
This paper addresses the study of the hierarchical control for the one-dimensional wave equation in intervals with a moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving. When…
Given a state space, Assignment of Observables involves Taking Function spaces Thereover. At the classical level, the state space in question is phase space or configuration space. This assignment picks up nontrivialities when whichever…
We prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$-order linear energy and the corresponding energy norm. In the…
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
This paper investigates the Cauchy problem of the time-space fractional Keller-Segel-Navier- Stokes model, which can describe both memory effect and L\'evy process of the system. The local existence and global existence in Lebesgue space…
In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally H\"older continuous. We first…
We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and apply them to obtain observability inequalities for its solutions over measurable sets.
We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not…
We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the…
In this work, we present an efficient approach for the spatial and temporal discretization of the nonlocal Allen-Cahn equation, which incorporates various double-well potentials and an integrable kernel, with a particular focus on a…
This work is devoted to the control of the Fokker-Planck equation, posed on a smooth bounded domain of R^d, with a localized drift force. We prove that this equation is locally controllable to regular nonzero trajectories. Moreover, under…
We prove global in time existence of solutions of the Euler compressible equations for a Van der Waals gas when the density is small enough in $\H{m}$, for $m$ large enough. To do so, we introduce a specific symmetrisation allowing areas of…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state…