Trace identities for solutions of the wave equation with initial data supported in a ball

Mathematical Methods in the Applied Sciences

Volumn 28, Issue 16, 2005, Pages 1897-1917

  Finch, David ^a   Rakesh, ^b  

^a OREGON STATE UNIVERSITY   (United States)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

Trace; Wave

Indexed keywords

BOUNDARY CONDITIONS; PROBLEM SOLVING; WAVE EQUATIONS;

IDENTITIES; INTEGRAL GEOMETRIC; MULTIPLIER METHODS; TRACES;

INITIAL VALUE PROBLEMS;

EID: 27144513453     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.647     Document Type: Article

References (12)

1. Finch D, Patch S, Rakesh. Determining a function from its mean values over a family of spheres. SIAM Journal on Mathematical Analysis 2004; 35(5):1213-1240.
2. Friedlander FG. Radiation fields and hyperbolic scattering theory. Mathematical Proceedings of the Cambridge Philosophical Society 1980; 88:483-515.
3. Bukhgeim AL, Kardakov VB. Solution of an inverse problem for an elastic wave equation by the method of spherical means. Siberian Mathematical Journal 1978; 19(4):528-535.
4. Bao G, Symes WW. A trace theorem for solutions of linear partial differential equations. Mathematical Methods in the Applied Sciences 1991; 14(8):553-562.
5. Bao G, Symes WW. Trace regularity for a second order hyperbolic equations with non-smooth coefficients. Journal of Mathematical Analysis and Applications 1993; 174:370-389.
6. Symes WW. A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources. Mathematical Methods in the Applied Sciences 1983; 5(2):131-152.
7. Lasiecka I, Triggiani R. Trace regularity of the solutions of the wave equation with homogeneous Neumann boundary conditions and data supported away from the boundary. Journal of Mathematical Analysis and Applications 1989; 141(1):49-71.
8. Lasiecka I, Triggiani R. Sharp regularity theory for second order hyperbolic equations of Neumann type. Annali de Matematica Pura ed Applicata 1990; 157(4):285-367.
9. Tataru D. On the regularity of boundary traces for the wave equation. Annali della Scuola Normale Superiore de Pisa Classe di Scienza 1998; 26(1):185-206.
10. Stein EM, Weiss G. Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press: Princeton, NJ, 1971.
11. Sakamoto R. Hyperbolic Boundary Value Problems. Cambridge University Press: Cambridge, 1982.
12. John F. Partial Differential Equations. Springer: Berlin, 1982.