Related papers: Solving the Linear 1D Thermoelasticity Equations w…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
We study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the…
In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability…
This work considers to numerically solve a subdiffusion equation involving constant time delay $\tau$ and Riemann-Liouville fractional derivative. First, a fully discrete finite element scheme is developed for the considered problem under…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
We study the large time behavior of solutions to a linear transmission problem in one space dimension. The problem at hand models a thermoelastic material with second sound confined by a purely elastic one. We shall characterize all…
This paper investigates the qualitative properties of thermoelastic plates modeled by the second-gradient theory with a Type I heat equation. We establish the exponential stability of the solutions. Our main contribution is to prove that…
In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal,…
When studying a general system of delay differential equation with a single constant delay, we encounter a certain lack of uniqueness in determining the coefficient of one of the third order terms of the series defining the center manifold.…
Differential equations with state-dependent delays define a semiflow of continuously differentiable solution operators in general only on an associated submanifold of the Banach space $C^1([-h,0],\mathbb{R}^n)$. We extend a recent result on…
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
The global well-posedness and stability of solutions to the three-dimensional compressible Euler equations with damping is a longstanding open problem. This problem was addressed in \cite{WY, STW} in the isentropic regime (i.e. $\gamma>1$)…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
In an open bounded interval $\Omega$, the problem \[ u_{tt} = u_{xx} - \big(f(\Theta)\big)_x, \Theta_t = \Theta_{xx} - f(\Theta) u_{xt}, \] is considered under the boundary conditions $u|_{\partial\Omega}=\Theta_x|_{\partial\Omega}=0$, and…
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for…
The problem of late time instability in time domain integral equations for electromagnetics is longstanding. While several techniques have been suggested for addressing this problem, they either require impractically high degrees of freedom…
We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…