相关论文: Quasistatic limit of a dynamic viscoelastic model …

Recently, for periodic initial data with initial density allowed to vanish, Huang and Li [1] establish the global existence of strong and weak solutions for the two-dimensional compressible Navier{Stokes equations with no restrictions on…

We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in…

Foams are unstable jammed materials. They evolve over timescales comparable to their "time of use", which makes the study of their destabilisation mechanisms crucial for applications. In practice, many foams are made from viscoelastic…

In this work, we present a novel approach to the mathematical analysis of equations with memory based on the notion of a state, namely, the initial configuration of the system which can be unambiguously determined by the knowledge of the…

Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…

We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic…

We study a variational model for the quasistatic growth of cracks with fractional di- mension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model…

The aim article is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type. A general framework suited for parabolic equations in one dimensional bounded…

This note is to conclude $L^1-L^1$ estimates for solutions to the following Cauchy problem for visco-elastic damped $\sigma$-evolution models: \begin{equation} \begin{cases} u_{tt}+ (-\Delta)^\sigma u+ (-\Delta)^\sigma u_t = 0, &\quad x\in…

The real area of contact governs, in part, the magnitude of the friction force, yet its time evolution in rough viscoelastic interfaces remains incompletely understood. In experiments of contact between polymethylmethacrylate blocks under…

We propose a mathematical model that combines elastic, viscous and porous effects with growth or shrinkage due to microstructural changes. This phenomenon is important in tissue or tumor growth, as well as in dermal contraction. Although…

The long- and short-time behavior of solutions to dissipative evolution equations is studied by applying the concept of hypocoercivity. Aiming at partial differential equations that allow for a modal decomposition, we compute estimates that…

We consider a second order equation with a linear "elastic" part and a nonlinear damping term depending on a power of the norm of the velocity. We investigate the asymptotic behavior of solutions, after rescaling them suitably in order to…

We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…

In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…

We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…

We study the following Cauchy problem for the linear wave equation with both time-dependent friction and time-dependent viscoelastic damping: \begin{equation} \label{EqAbstract}\tag{$\ast$} \begin{cases} u_{tt}- \Delta u + b(t)u_t -…

We review the task of aligning simple models for language dynamics with relevant empirical data, motivated by the fact that this is rarely attempted in practice despite an abundance of abstract models. We propose that one way to meet this…