We consider a one-phase Stefan problem for the heat equation with a superlinear reaction term. It is known from a previous work (Ghidouche, Souplet, & Tarzia [5]) that all global solutions are bounded and decay uniformly to 0. Moreover, it was shown in Ghidouche, Souplet, & Tarzia [5] that either: (i) the free boundary converges to a finite limit and the solution decays at an exponential rate, ...

Abstract We study discrete random Schrödinger operators via the supersymmetric formalism. develop a cluster expansion that converges at both strong and weak disorder. prove exponential decay of disorder-averaged Green’s function smoothness local density states either disorder energies in proximity unperturbed spectrum or any energy. As an application, we establish Lifshitz-tail-type estimates f...

In this article we investigate hypocoercivity of Langevin-type dynamics in nonlinear smooth geometries. The main result stating exponential decay to an equilibrium state with explicitly computable rate convergence is rooted appealing Hilbert space strategy by Dolbeault, Mouhot and Schmeiser. This was extended Grothaus Stilgenbauer (2014) Kolmogorov backward evolution equations contrast the dual...

<p style='text-indent:20px;'>We consider dispersing billiard tables whose boundary is piecewise smooth and the free flight function unbounded. We also assume there are no cusps. Such called type D in monograph of Chernov Markarian [<xref ref-type="bibr" rid="b9">9</xref>]. For a class non-degenerate billiards, we prove exponential decay correlation several other statistical pr...

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For wider class relaxation functions, We show that dissipation produced memory eect strong enough to produce general decay results. establish results, from which usual exponential polynomial rates are only special cases.

The influence of exponential magnetic field decay (MFD) on the spin evolution of isolated neutron stars is studied. The ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars, are used to constrain the exponential and power-law decay parameters. We show that for the exponential decay the ranges of minimum value of magnetic moment, μb, and the characterist...

Transient signals naturally arise in numerous disciplines for which the decay rates and amplitudes carry some informational significance. Even when the decay rates are known, solving for the amplitudes results in an ill-conditioned formulation. Transient signals in the presence of noise are further complicated as the signal-to-noise ratio asymptotically decreases in time. In this thesis the Dis...