相关论文: On the effectiveness of Gamow's method for calcula…

We consider solutions to the initial value problem associated to the intermediate long wave (ILW) equation. We establish persistence properties of the solution flow in weighted Sobolev spaces, and show that they are sharp. We also deal with…

In this paper, we study the Moore--Gibson--Thompson equation in $\mathbb{R}^N$, which is a third order in time equation that arises in viscous thermally relaxing fluids and also in viscoelastic materials (then under the name of…

We consider the Cauchy problems in the whole space for the wave equation with a weighted L^{1}-initial data. We first derive sharp infinite time blowup estimates of the L^{2}-norm of solutions in the one and two dimensional cases. Then, we…

We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced.…

We give a simple proof of a pointwise decay estimate in 3+1 dimensions stated in two versions, making advantage of a particular simplicity of inverting the spherically symmetric part of the wave operator and of the comparison theorem. We…

The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay…

In the paper, a simple model of alpha decay with Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to power law behavior at asymptotic times. Time dependence of the survival probability of the…

Harnessing the abstract power of the celebrated result due to Borichev and Tomilov (Math.\ Ann.\ 347:455--478, 2010, no.\ 2), we study the energy decay in a one-dimensional coupled wave-heat-wave system. We obtain a sharp estimate for the…

The optimality of decay properties of the one-dimensional damped wave equations with potentials belonging to a certain class is discussed. The typical ingredient is a variant of Nash inequality which involves an invariant measure for the…

We prove a weighted a priori energy estimate for the two dimensional water-waves problem with contact points in the absence of gravity and surface tension. When the surface graph function and its time derivative have some decay near the…

We study the wave equation with potential $u_{tt}-\Delta u+Vu=0$ in two spatial dimensions, with $V$ a real-valued, decaying potential. With $H=-\Delta+V$, we study a variety of mapping estimates of the solution operators, $\cos(t\sqrt{H})$…

The calculation of the decay rate of a metastable state in the path-integral formulation of stochastic processes is revisited. Previous derivations of this rate were achieved at the cost of a step that is difficult to justify…

We obtain the precise form of two Gamow functionals, representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing…

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrodinger…

We studed alpha decay half-lives of Pb isotopes in the range 178 < A > 220, whithin Gamow-like model (GLM) which is based on Gamow theory. The empirical formulae like Royer formula, Universal Decay Low (UDL), Viola-Seaborg formula (VSS),…

We consider the Cauchy problem for wave equations with variable coefficients in the whole space. We improve the rate of decay of the local energy, which has been recently studied by J. Shapiro, where he derives the log-order decay rates of…

We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The proof is based on a similar strategy as in Dyatlov-Jin and in…

It is known that the asymptotic behavior of time-dependent dissipative coefficient in the Cauchy problem of dissipative wave equation dominates the energy decay estimate. In particular, it is important to study the case where the…

We address the study of decay rates of solutions to dissipative equations. The characterization of these rates is given for a wide class of linear systems by the {\em decay character}, which is a number associated to the initial datum that…

We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…