Stability and Controllability of Differential Equations

Abstract We consider inverse problems of determining a spatially varying coefficient or spatially varying factor in a source term from the initial and final data together and Cauchy data on a lateral boundary. We establish both uniqueness and the stability results. The key idea is a simple translation with respect to…

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We study a nonlinear Steklov problem involving weighted p(.)-Laplacian-like operator. Using some variational methods, we obtain the existence and multiplicity of solutions for the following problem $$\begin{aligned} \left\{ \begin{array}{cc} \text {div}\left( \left( 1+\frac{\left| \nabla u\right| ^{p(x)}}{ \sqrt{1+\le…

ABSTRACT We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of Forchheimer‐type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a nonlinear partial differential equation for the pseudo‐pressure. This parab…

ABSTRACT This paper investigates a class of nonlinear plate equations with the ‐Laplacian operator and a nonlocal damping term in the presence of a variable‐exponent logarithmic source. Using the Faedo‐Galerkin approximation, we establish the existence of local weak solutions. Subsequently, after demonstrating that th…

In this paper, we consider control constrained $L^2-$Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the control problem based on the local discontinuous Galerkin method with piecewise linear ansatz functions for the flux and potential. We deriv…

In this paper, we consider control constrained $L^2-$Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the control problem based on the local discontinuous Galerkin method with piecewise linear ansatz functions for the flux and potential. We deriv…

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A class of Kuramoto models with a general coupling function that can be expressed in terms of a finite number of harmonics, each comprising sinusoidal terms, is studied. We propose a novel approach for certifying local phase synchronization in this class for all initial conditions lying on an arc. The trace parametriz…

A class of Kuramoto models with a general coupling function that can be expressed in terms of a finite number of harmonics, each comprising sinusoidal terms, is studied. We propose a novel approach for certifying local phase synchronization in this class for all initial conditions lying on an arc. The trace parametriz…

We develop a method for constructing Lyapunov functions via Semidefinite Programming (SDP) that certifies the stability of oscillatory systems with both Cartesian and angular variables. We utilize the theory of hybrid polynomials (also called mixed trigonometric-polynomials) introduced by Dumitrescu. We use this theor…