Related papers: Multidimensional decay in van der Corput lemma
We study the evolution of the universe which contains a multiple number of non-relativistic scalar fields decaying into both radiation and pressureless matter. We present a powerful analytic formalism to calculate the matter and radiation…
We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution…
We study polynomial stability to the one-dimensional system in the linear isothermal theory of swelling porous elastic soils with an internal fractional damping. We establish an optimal decay result by frequency domain method
This paper studies the one dimensional Navier-Stokes-Fourier-Korteweg system of equations describing the evolution of a heat-conducting compressible fluid that exhibits viscosity and capillarity. The main goal of the present analysis is to…
The phase space of $N$ damped linear oscillators is endowed with a bilinear map under which the evolution operator is symmetric. This analog of self-adjointness allows properties familiar from conservative systems to be recovered, e.g.,…
Dilative stability generalizes the property of selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. Inspired by results of Igl\'oi, we will show how dilatively stable…
We extend the quantum theory of dissipation in the context of system-reservoir model, where the reservoir in question is kept in a nonequilibrium condition. Based on a systematic separation of time scales involved in the dynamics,…
Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in…
Semileptonic decays of D-mesons into scalar hadronic states are investigated. Two extreme cases are considered: a) the meson decays directly into an uncorrelated scalar state of two two mesons and b) the decay proceeds via resonance…
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…
We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, $d=d_\parallel+d_\perp$, being $d_\parallel$ the dimension of the parallel space spanned by the legs of the…
We prove a general asymptotic decay lemma which is applicable in various contexts. As an example, the general theorem is shown to give lower growth estimates for entire and exterior solutions of the minimal surface equation.
The critical constant of time-decaying damping in the scale-invariant case is recently conjectured. It also has been expected that the lifespan estimate is the same as for the associated semilinear heat equations if the constant is in the…
Structure of the eigenfrequencies parameter space for three and four dissipatively coupled van der Pol oscillators is discussed. Situations of different codimension relating to the configuration of the full synchronization area as well as a…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
We theoretically investigate two quantum modes interacting via local couplings to a dissipative field. Our model considers two mechanical modes with distinct frequencies coupled optomechanically to the same cavity mode. The dissipative…
We apply the monotone domain decomposition iterative method to a nonlinear integro-differential equation of Volterra type and prove its convergence. To do this, by adding a term in both sides of the original equation we make a linear…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
In this paper we study a class of semilinear wave type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able…
The scaling properties of a phase-ordering system with a conserved order parameter are studied. The theory developed leads to scaling functions satisfying certain general properties including the Tomita sum rule. The theory also gives good…