Solution of Biharmonic Equations with Application to Radar Imaging
نویسنده
چکیده
In a radar imaging problem using broad-band, low-frequency waves, we encounter the problem of solving Poisson's equation over a very large rectangular grid, typically ve thousand times thousand pixels. In addition, no information about boundary values is available. In order to select suitable solutions we solve the Poisson equation under the side condition that some criterion function, usually a Sobolev norm, should be minimized. Under appropriate smoothness assumptions this problem may be reformulated as a boundary value problem for the biharmonic equation. Numerical techniques are investigated for this problem. We also include the results of some numerical experiments.
منابع مشابه
Bifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations
In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...
متن کاملApproximate solution of boundary integral equations for biharmonic problems in non-smooth domains
This paper deals with approximate solutions to integral equations arising in boundary value problems for the biharmonic equation in simply connected piecewise smooth domains. The approximation method considered demonstrates excellent convergence even in the case of boundary conditions discontinuous at corner points. In an application we obtain very accurate approximations for some characteristi...
متن کاملFirst Principles Derivation of Displacement and Stress Function for Three-Dimensional Elastostatic Problems, and Application to the Flexural Analysis of Thick Circular Plates
In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...
متن کاملMultiple solutions for a perturbed Navier boundary value problem involving the $p$-biharmonic
The aim of this article is to establish the existence of at least three solutions for a perturbed $p$-biharmonic equation depending on two real parameters. The approach is based on variational methods.
متن کاملThe decomposition method for one dimensional biharmonic equations
Abstract: This paper deals with the study of the numerical solution of biharmonic equations in one dimension. Biharmonic equations appear frequently in many areas of engineering and physics representing some phenomena. The solution of such problems have been tackled by many authors. In this paper, a numerical method based on the Adomian decomposition method is introduced for the approximate sol...
متن کامل