Inverse Source Problems for the Stochastic Wave Equations: Far-Field Patterns

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Far Field Expansion for Anisotropic Wave Equations

Uncertainty Principles for Inverse Source Problems, Far Field Splitting, and Data Completion

The next lemma shows that odd and even rescaled squared singular values, sn(R), are monotonically decreasing for n ≥ 0 and monotonically increasing for n ≤ 0. ∗Submitted to the editors July 22, 2016. †Institut für Mathematik, Universität Würzburg, 97074 Würzburg, Germany ([email protected]). ‡Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A....

Inverse Source Problems in Transport Equations

Abstract. This paper proposes an iterative technique to reconstruct the source term in transport equations, which account for scattering effects, from boundary measurements. In the two-dimensional setting, the full outgoing distribution in the phase space (position and direction) needs to be measured. In three space dimensions, we show that measurements for angles that are orthogonal to a given...

Identification - - Inverse Problems for Partial Differential Equations : a Stochastic Formulation

This paper presents a stochastic formulation of a class of identification problems for partial differential equations, known as 'inverse' problems in the mathematicalphysics literature. By introducing stochastic processes to model errors in observation as well as 'disturbance' we can provide a precise formulation to interpret what appear to be 'ad hoc' techniques, especially in the treatment of...