1,721,035 research outputs found
A hierarchy of heat conduction laws
No full textThe purpose of this work is to produce a family of equations describing the evolution of the temperature in a rigid heat conductor. This is obtained by means of successive approximations of the Fourier law, via memory relaxations and integral perturbations
A one-dimensional wave equation with nonlinear damping
No full textWe consider a one-dimensional weakly damped wave equation, with a damping coefficient depending on the displacement. We prove the existence of a regular connected global attractor of finite fractal dimension for the associated dynamical system, as well as the existence of an exponential attractor
Second Order Linear Evolution Equations with General Dissipation
Full text linkThe contraction semigroup S(t) = etA generated by the abstract linear dissipative evolution equation u ̈+Au+f(A)u ̇=0is analyzed, where A is a strictly positive selfadjoint operator and f is an arbitrary nonnegative continuous function on the spectrum of A. A full description of the spectrum of the infinitesimal generator A of S(t) is provided. Necessary and sufficient conditions for the stability, the semiuniform stability and the exponential stability of the semigroup are found, depending on the behavior of f and the spectral properties of its zero-set. Applications to wave, beam and plate equations with fractional damping are also discussed
On the strongly damped wave equation with memory
No full textA semilinear strongly damped wave equation with memory is considered in the past history framework. The existence of global attractors of optimal regularity is established, both for critical and supercritical nonlinearities, under a necessary and sufficient condition on the memory kernel
Navier-Stokes limit of Jeffreys type flows
No full textWe analyze a Jeffreys type model ruling the motion of a viscoelastic polymeric solution with linear memory in a two-dimensional domain with nonslip boundary conditions. For fixed values of the concentrations, we describe the asymptotic dynamics and we prove that, when the scaling parameter in the memory kernel (physically, the Weissenberg number of the flow) tends to zero, the model converges in an appropriate sense to the Navier-Stokes equations
ON THE OPTIMAL DECAY RATE OF THE WEAKLY DAMPED WAVE EQUATION
No full textWe provide a proof via direct energy estimates of the optimal exponential decay rate of the semigroup generated by the weakly damped wave equation
Nonclassical diffusion with memory lacking instantaneous damping
No full textWe consider the nonclassical diffusion equation with hereditary memory (Formula Presented) on a bounded three-dimensional domain. The main feature of the model is that the equation does not contain a term of the form −∆u, contributing as an instantaneous damping. Setting the problem in the past history framework, we prove that the related solution semigroup possesses a global attractor of optimal regularity
Space and time estimates of second gradient thermal problems
No full textWe consider the space and time decays of certain problems within the second gradient thermal law. Notably, for this thermal theory, the exponential time decay is precluded. First, the time estimates of polynomial type are obtained for both the thermal equation and the one-dimensional thermoelastic system, where the impossibility of localization with respect to time is also established. Then, the space estimates are deduced for the multidimensional thermoelastic problem, which allow to show the exponential decay of the energy
Trajectory and global attractors for evolution equations with memory
No full textOur aim in this note is to analyze the relation between two notionsof attractors for the study of the long time behavior of equationswith memory, namely, the global attractor in the so-called pasthistory approach, and the more recently proposed notion of trajectory attractor
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