A fundamental solution of the acoustical equation with a variable refraction coefficient is constructed. The solution satisfies the limiting absorption and radiation conditions. The optimal high frequency estimate is proved for square means of the solution. The source function for the diffusion equation is a by-product of this construction.
Partially supported by a stipend of the Mathematical Scientific Research Institute at Berkeley, 2001.
"Fundamental solutions of the acoustic and diffusion equations in nonhomogeneous medium." Ark. Mat. 42 (1) 119 - 152, April 2004. https://doi.org/10.1007/BF02432913