Finite element methods for Maxwell's equations.

Preface 1. Fourier series and Fourier transforms 2. Distributions 3. Elliptic equations (fundamental theory) 4. Initial value problems (Cauchy problems) 5. Evolution equations 6. Hyperbolic equations 7. Semi-linear hyperbolic equations 8. Green's functions and spectra Supplementary remarks Guide to the literature Bibliography Symbols Index.

The theory of partial differential equations

Proceedings of the American Mathematical Society

Thank you very much for downloading integral equation methods in scattering theory. Maybe you have knowledge that, people have look numerous times for their favorite readings like this integral equation methods in scattering theory, but end up in malicious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they juggled with some harmful virus inside their laptop. integral equation methods in scattering theory is available in our book collection an online access to it is set as public so you can download it instantly. Our books collection saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the integral equation methods in scattering theory is universally compatible with any devices to read.

Integral Equation Methods In Scattering Theory

This chapter is concerned with the introduction of the basic integral equations for two-dimensional elastic linear material problems. It starts by briefly reviewing the partial differential equations for linear elastic material and introducing the necessary notations involved in the formulation. These governing equations are also extended to deal with problems in which initial stress and strain type loads are applied. Such kind of loads are not only important to take into account temperature or other similar loads, but also to model nonlinear material behaviour when used in conjunction with a well established successive elastic solution technique.

Boundary Integral Equations

In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded...

The Calderón problem for a space-time fractional parabolic equation

We consider an inverse problem for the fractional Schrodinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their...

Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials

In this work, we study the inverse source problem of a fixed frequency for the Navier equation. We investigate non-radiating external forces. If the support of such a force has a convex or non-convex corner or edge on its boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: an energy identity and a new type of exponential solution for the Navier equation.

/pdf/radiating-and-non-radiating-sources-in-elasticity-3cehey6253.pdf

Radiating and non-radiating sources in elasticity

We consider the inverse problems of for the fractional Schrodinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calderon problem in a constructive manner. Secondly, we offer a reconstruction method for an unknown obstacles in a given domain. Our method is independent of the dimension $n\geq 2$ and only requires the background solution of the fractional Schrodinger equation.

Monotonicity-based inversion of the fractional Schr\"odinger equation I. Positive potentials

We introduce a method for solving Calderon type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension $2$, and a potential on transversally anisotropic manifolds in dimensions $n \geq 3$. In the Euclidean case, we show that one can solve the Calderon problem for certain semilinear equations in a surprisingly simple way without using complex geometrical optics solutions.

Yi-Hsuan Lin

Papers

The Calderón problem for a space-time fractional parabolic equation

Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials

Radiating and non-radiating sources in elasticity

Monotonicity-based inversion of the fractional Schr\"odinger equation I. Positive potentials

Inverse problems for elliptic equations with power type nonlinearities