Related papers: Perturbation Methods and First Order Partial Diffe…

In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper \cite{DehmanLebeau09} to prove that: the weak…

We present a perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing by colored noise. In particular, the forcing arises from passing white noise through an $n$th order…

Consider in a real Hilbert space $H$ the differential equation (inclusion) $(E)$: $p(t)u^{\prime \prime}(t)+q(t)u^{\prime}(t)\in Au(t)+f(t)$ for a.a. $t>0$, with the condition $(B)$: $u(0)=x \in \overline{D(A)}$, where $A\colon D(A)\subset…

We address the linear-mode analysis performed near an equilibrium configuration in the fluid rest frame with a dynamical magnetic field perturbed on a constant configuration. We develop a simple and general algorithm for an analytic…

The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…

Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth differential equations was developed in terms of Brouwer degree theory. Between the…

A system of first-order differential equations for a particle with nonzero mass and spin $S = 1$ is constructed. As distinct from the Proca-Duffin-Kemmer (PDK) equations, the system has the form of the dynamical equation…

In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a…

There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions and might fail after several steps, or are restricted to…

We present a perturbation-based framework that captures buoyancy effects on modal instabilities in stratified boundary-layer flows within the fully compressible, non-Oberbeck-Boussinesq formulation. Treating the Richardson number as a small…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…

In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…

This paper is concerned with H\"older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain,…

Hyperbolic systems of the first and higher-order partial differential equations appear in many multiphysics problems. We will be dealing with a wave propagation problem in a piece-wise homogeneous medium. Mathematically, the problem is…

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…

In this paper we use the Riccati equation method with other ones to establish global solvability, stability and oscillation criteria for a class of two dimensional nonlinear systems of ordinary differential equations, which is a…

A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…

This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…

We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…