may be thought of as a nonlinear beam equation. In this paper we obtain both L-L estimates and space-time integrability estimates on solutions to the linear equation. We also use these estimates to study the local existence and asymptotic behavior of solutions to the nonlinear equation, for nonlinear terms which grow like a certain power of u. The main L-L estimate (Theorem 2.1) states that sol...

one deals with time evolution problem, which does not improve smoothness with time. This simple but very fundamental observation (in sharp contrast with the better behaved parabolic evolution) has necessitated radically different approach to the standard questions of local and global well-posedness, persistence of smoothness, stability of localized structures etc. Indeed, tackling these questio...

Abstract. We show decay estimates for the propagator of the discrete Schrödinger and Klein-Gordon equations in the form ‖U(t)f‖l∞ ≤ C(1 + |t|)‖f‖l1 . This implies a corresponding (restricted) set of Strichartz estimates. Applications of the latter include the existence of excitation thresholds for certain regimes of the parameters and the decay of small initial data for relevant l norms. The an...

We show decay estimates for the propagator of the discrete Schrödinger and Klein–Gordon equations in the form ‖U(t)f ‖l∞ C(1 + |t |)−d/3‖f ‖l1 . This implies a corresponding (restricted) set of Strichartz estimates. Applications of the latter include the existence of excitation thresholds for certain regimes of the parameters and the decay of small initial data for relevant l norms. The analyti...

In this work decay estimates are derived for the solutions of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The decay estimates are given in the 2 L and 1 H norms of the solution and discontinuous disturbances are allowed. Although an eigenfunction expansion for the solution is exploited for the proof of the decay estimates, the estimates do not re...

In this paper, we introduce a new multivariate Weibull (MVW) distribution with many interesting properties. We obtain the maximum likelihood estimate (MLE) of the parameters and their asymptotic multivariate normal (AMVN) distribution in MVWmodel. We propose large sample studentized tests for testing multivariate exponentiality and also tests for independence and identical marginals of the comp...

We study generalizations of Agmon-type estimates on eigenfunctions for Schrödinger operators. In the first part, we prove an exponential decay estimate on eigenfunctions for a class of pseudodifferential operators. In the second part, we study the semiclassical limit of ~-pseudodifferential operators, and exponential decay estimates on eigenfunctions and Briet-Combes-Duclos-type resolvent estim...