Related papers: A note on asymptotic profiles for the thermoelasti…
In this section, we consider the heat equation on a plate with thickness h > 0 being heated by a heat source on upper and lower faces of the plate. We obtain an asymptotic profile of the solution as the thickness h > 0 approaches to zero.
We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour…
The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the…
At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of…
We review an scenario for the non-equilibrium dynamics of glassy systems that has been motivated by the exact solution of simple models. This approach allows one to set on firmer grounds well-known phenomenological theories. The old ideas…
The objective of the present paper is to investigate the decay of solutions for a laminated Timoshenko beam with interfacial slip in the whole space R subject to a thermal effect acting only on one component modelled by either Fourier or…
Understanding glasses is considered to be one of the most fundamental problems in statistical physics. A theoretical approach to unravel their universal properties is to consider the validity of equilibrium concepts such as temperature and…
We consider the Cauchy problems in n-dimensional Euclidean space for the plate equation with a weighted L^{1}-initial data. We derive optimal estimates of the L^{2}-norm of solutions for n = 1, 2, 3, 4. In particular, such obtained results…
We show that computing the coefficients of the Taylor expansion of the solution of the off-equilibrium dynamical equations characterizing models with quenched disorder is a very effective way to understand the long time asymptotic behavior.…
In this paper we investigate the asymptotic behavior and decay of the solution of the discrete in time $N$-dimensional heat equation. We give a convergence rate with which the solution tends to the discrete fundamental solution, and the…
The dynamics of interacting bosons in one dimension following the sudden switching on of a weak disordered potential is investigated. On time scales before quasiparticles scatter (prethermalized regime), the dephasing from random elastic…
An asymptotic expansion with respect to a small parameter of the solution of the Cauchy problem is constructed for a system of three transfer equations, two of which are singularly perturbed by the degeneracy of the entire senior part of…
We study the glassy dynamics taking place in dense assemblies of athermal active particles that are driven solely by a nonequilibrium self-propulsion mechanism. Active forces are modeled as an Ornstein-Uhlenbeck stochastic process,…
We consider the Cauchy problem on nonlinear scalar conservation laws with a diffusion-type source term related to an index $s\in \R$ over the whole space $\R^n$ for any spatial dimension $n\geq 1$. Here, the diffusion-type source term…
In this paper, we study the Cauchy problem for a wave equation with general strong damping $-\mu(|D|)\Delta u_t$ motivated by [Tao, Anal. PDE (2009)] and [Ebert-Girardi-Reissig, Math. Ann. (2020)]. By employing energy methods in the Fourier…
Previous experiments and numerical simulations have revealed that a limited number of two- and three-dimensional particle systems contract in volume upon heating isobarically. This anomalous phenomenon is known as negative thermal expansion…
We develop a theory of the effective disorder temperature in glass-forming materials driven away from thermodynamic equilibrium by external forces. Our basic premise is that the slow configurational degrees of freedom of such materials are…
We study the large time behavior of nonnegative solutions to the Cauchy problem for a fast diffusion equation with critical zero order absorption $$ \partial_{t}u-\Delta u^m+u^q=0 \quad \quad \hbox{in} \ (0,\infty)\times\real^N\, $$ with…
We prove the well-posedness of the Cauchy problem on torus to an eletromagnetoelastic system. The physical model consists of three coupled partial differential equations, one of them is a hyperbolic equation describing the elastic medium…
In this paper, we are interested in the Cauchy problem for the viscoelastic damped wave equation with memory of type I. By applying WKB analysis and Fourier analysis, we explain the memory's influence on dissipative structures and…