Related papers: Well-posedness of time-varying linear systems

A linear stochastic vector advection equation is considered. The equation may model a passive magnetic field in a random fluid. The driving velocity field is a integrable to a certain power and the noise is infinite dimensional. We prove…

This paper addresses the problem of wellposedness of non-autonomous linear evolution equations $\dot x = A(t)x$ in uniformly convex Banach spaces. We assume that $A(t):D \subset X\to X$, for each $t$ is the generator of a quasi-contractive…

We establish probabilistic well-posedness results for the subcubic nonlinear wave equation, posed on the domain $B_2\times\mathbb{T}$, with randomly chosen initial data having radial symmetry in the $B_2$ variable, and with vanishing…

We consider the linear transport equation with a globally Holder continuous and bounded vector field. While this deterministic PDE may not be well-posed, we prove that a multiplicative stochastic perturbation of Brownian type is enough to…

We derive a sufficient condition guaranteeing that a singularly perturbed linear time-varying system is strongly monotone with respect to a matrix cone $C$ of rank $k$. This implies that the singularly perturbed system inherits the…

This work concerns a type of path-dependent multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the well-posedness for path-dependent multivalued stochastic differential equations under the Lipschitz…

In the present paper, we consider second order strictly hyperbolic linear operators of the form $Lu\,=\,\partial_t^2u\,-\,{\rm div}\big(A(t,x)\nabla u\big)$, for $(t,x)\in[0,T]\times\mathbb{R}^n$. We assume the coefficients of the matrix…

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…

In this paper, we examine the shifted passivity property of port-Hamiltonian systems. Shifted passivity accounts for the fact that in many applications the desired steady-state values of the input and output variables are nonzero, and thus…

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…

We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…

We consider the Cauchy problem of a system of quadratic derivative nonlinear Schr\"odinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic case, the author proved…

We consider bimodal planar switched linear systems and obtain dwell time bounds which guarantee their asymptotic stability. The dwell time bound obtained is a smooth function of the eigenvectors and eigenvalues of the subsystem matrices. An…

In this short paper, we prove a well-posedness theorem for the massive wave equation (with the mass satisfying the Breitenlohner-Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed as a limit of solutions to…

This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under the…

In this paper, we investigate the well-posedness of the martingale problem associated to non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under mild assumptions on the coefficients as well as classical…

The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in…

A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…

We study the well-posedness of the Cauchy problem with Dirichlet or Neumann boundary conditions associated to an H 1 -critical semilinear wave equation on a smooth bounded 2D domain {\Omega}. First, we prove an appropriate Strichartz type…

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the…