Stability estimates for diverse inverse source problems in time-domain elastic wave equations

Abstract We are concerned with the stability of the inverse source problem for the elastic wave equation from boundary Dirichlet data in the full space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℝ</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> {{\mathbb{R}}^{3}} . When source term has special form and compact supports, the stability estimates are obtained. Our results show for the first time that the stability estimates of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> {L^{2}} -norm of source function can be established by using only the Dirichlet boundary data. The main goal of this paper is to understand the stability for the elastic wave equation in the time domain.