Showing papers on "A priori estimate published in 1994"

Generalizations of the non‐linear ocean‐SAR transform and a simplified SAR inversion algorithm

Abstract: It is demonstrated that the non‐linear transform from the ocean wave spectrum to the synthetic aperture radar (SAR) image spectrum may be extended to include point target spreading (dispersive) effects. For practical purposes, the extension amounts to an additional azimuth spectral cut‐off factor applied to the result of the velocity bunching nonlinear transform without point‐target dispersion. The validity of a quasi‐linear approximation is analysed by means of simple Gaussian test spectra, which also reveal the nature of the fully non‐linear velocity bunching transform. The inversion problem is formulated as a constrained functional minimization over non‐negative wave spectra. An iterative solution method that requires an a priori estimate of the wave spectrum is demonstrated. Analysis of the method leads to a simple theory for preparing the necessary weight functions for the observed SAR and the a priori wave spectra. Combined with an optimized quasi‐linear ocean‐SAR transform, the new formula...

A free boundary problem modeling thermal instabilities: well-posedness

Abstract: In this paper, the authors analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures many salient features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The main result is a global existence and uniqueness theorem whose proof is based on a uniform a priori estimate on the growth of solutions. The techniques employed are quite elementary and involve some maximum principle type estimates as well as parabolic potential estimates for the equivalent integral equation.

Global strong solvability of Dirichlet problem for a class of nonlinear elliptic equations in the plane

Abstract: Global solvability and uniqueness results are established for Dirichlet's problem for a class of nonlinear differential equations on a convex domain in the plane, where the nonlinear operator is elliptic in sense of Campanato. We prove existence by means of the Leray-Schauder fixed point theorem, using Alexandrov-Pucci maximum principle in order to find a priori estimate for the solution.

Derivation of 3d Navier-Stokes length scales from a result of Foias, Guillope and Temam

Abstract: Using estimates of Foias, Guillope and Temam(1981), who found an infinite set of a priori bounded time integrals of norms, two types of natural inverse length scale for solutions of the 3d periodic Navier-Stokes equations are introduced which are different from the inverse Kolmogorov length. The first is formed from a ratio of time averaged semi-norms, while the second is formed from a time average of a ratio of semi-norms. If G is the 3d Grashof number, then the best available a priori estimate for each of these two quantities is G2, leading to an estimate of G6 for the number of degrees of freedom in the system.

Line model for multisignature Gibbs classification

Abstract: The performance of the Gibbs Classifier over a statistically heterogeneous image can be improved if the locally stationary regions in the image are disassociated from each other through the mechanism of the interaction parameters defined at the local neighborhood level. This usually involves the construction of a line process for the image. In this paper we describe a method for constructing a line process for multisignature images based on the differential (total derivative) of the image which, when expressed statistically, can provide an a priori estimate of the line field.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A priori estimates to the maximum modulus of generalizedsolutions of a class of quasilinear elliptic equationswith anisotropic growth conditions

Abstract: In this paper we give a priori estimates for the maximum modulus of generalized solutions of the quasilinear elliptic equations with anisotropic growth condition