On solvability of an indefinite Riccati equation [PDF]
arXiv, 2013 This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is derived, based on a monotonicity property of a newly defined set.
arxiv
The global well-posedness and global attractor for the solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivity [PDF]
arXiv, 2014 Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature are proved.
arxiv
The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case. [PDF]
Chaos Solitons Fractals, 2022 Sabbar Y +3 more
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Almost Automorphy and Riccati Equation [PDF]
arXiv, 2014 In this paper we first consider a linear time invariant systems with almost periodic forcing term. We propose a new deterministic quadratic control problem, motivated by Da-Prato. With the help of associated degenerate Riccati equation we study the existence and uniqueness of an almost automorphic solutions.
arxiv
On Solving the Cauchy Problem with Propagators [PDF]
arXiv, 2014 The abstract first order Cauchy problem is solved in terms of Taylor's series leading to a series of operators which is a propagator. It is found that higher order Cauchy problems can be solved in the same way. Since derivatives of order lower than the Cauchy problem are built-in to the problem, it suffices to solve the higher order derivatives in ...
arxiv
Existence and data dependence results for fractional differential equations involving atangana-baleanu derivative. [PDF]
Rend Circ Mat Palermo, 2022 Sutar ST, Kucche KD.
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An Alternate Method for Finding Particular Solutions of Nonhomegeneous Differential Equations [PDF]
arXivIn this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every standard Differential Equations textbook.
arxiv
A Closed-Form Solution to the Arbitrary Order Cauchy Problem with Propagators [PDF]
arXiv, 2014 The general abstract arbitrary order (N) Cauchy problem was solved in a closed form as a sum of exponential propagator functions. The infinite sparse exponential series was solved with the aid of a homogeneous differential equation. It generated a linear combination of exponential functions.
arxiv
Diffeomorphism groups of compact convex sets [PDF]
arXiv, 2016 For a compact convex subset K with non-empty interior in a finite-dimensional vector space, let G be the group of all smooth diffeomorphisms of K which fix the boundary of K pointwise. We show that G is a C^0-regular infinite-dimensional Lie group. As a byproduct, we obtain results concerning solutions to ordinary differential equations on compact ...
arxiv
The Liouville Formula for the Uncertain Homogeneous Linear System and Explicit Solutions of the System. [PDF]
Differ Equ Dyn Syst, 2021 Roomi V, Ahmadi HR.
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