“Farfield” behavior of solutions to partial differential equations : asymptotic expansions and maximal rates of decay along a ray

Orazio Arena; Walter Littman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1972)

  • Volume: 26, Issue: 4, page 807-827
  • ISSN: 0391-173X

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Arena, Orazio, and Littman, Walter. "“Farfield” behavior of solutions to partial differential equations : asymptotic expansions and maximal rates of decay along a ray." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.4 (1972): 807-827. <http://eudml.org/doc/83619>.

@article{Arena1972,
author = {Arena, Orazio, Littman, Walter},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {807-827},
publisher = {Scuola normale superiore},
title = {“Farfield” behavior of solutions to partial differential equations : asymptotic expansions and maximal rates of decay along a ray},
url = {http://eudml.org/doc/83619},
volume = {26},
year = {1972},
}

TY - JOUR
AU - Arena, Orazio
AU - Littman, Walter
TI - “Farfield” behavior of solutions to partial differential equations : asymptotic expansions and maximal rates of decay along a ray
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1972
PB - Scuola normale superiore
VL - 26
IS - 4
SP - 807
EP - 827
LA - eng
UR - http://eudml.org/doc/83619
ER -

References

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  1. A. Friedman; [1] Partial Differential Equations, New York1969. Zbl0224.35002MR445088
  2. R. Goodman; [1] Causal S-operators and domains of dependence for hyperbolic equations, Thesis M. I. T. 1963. 
  3. R. Goodman; [2] One sided invariant subspace and domains of uniqueness for hyperbolic equations, Proc. AMS15 (1964), 653-660. Zbl0132.35706MR170119
  4. V.V. Gru; [1] On Sommerfeld-type conditions, Mat. Sb. (N. S.)61 (103) (1963), 147-174 (Russian). MR157106
  5. L. Hörmander; [1] Linear partial differential operators, Springer-Verlag, New York1969. Zbl0175.39201MR248435
  6. S.N. Karp; [1] A convergent «far-field» expansion for two-dimensional radiation functions, Comm. Pure Appl. Math.14 (1961), 427-434. Zbl0117.29802MR135451
  7. J.L. Lions; [1] Supports dans la transformation de Laplaoe, J. Analyse Math.2 (1953), 369-380. Zbl0051.33504MR58013
  8. W. Littman; [1] Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. AMS69 (1963), 766-770. Zbl0143.34701MR155146
  9. W. Littman; [2] Maximal rates of decay of solutions of partial differential equations, Archive Rat. Mech. Anal.37 (1970), 11-20. Zbl0215.45203MR257547
  10. K. Masuda; [1] On the exponential decay of solutions for some partial differential equatione, J. Math. Soc. Japan19 (1967), 82-90. Zbl0148.34603MR204827
  11. K. Masuda; [2] Asymptotic behavior in time of solutions for evolution equations, J. Funct. Anal.1 (1967), 84-92. Zbl0152.34001MR218733
  12. N. Meyers; [1] An expansion about infinity of solutions of linear elliptic equations, J. Math and Mech12 (1963), 247-264. Zbl0121.32202MR149072
  13. C. Morawetz; [1] A uniqueness theorem for the relativistic wave equation, Comm. Pure Appl. Math.16 (1963), 353-362. Zbl0117.06402MR162057
  14. M. Morse; [1] The calculus of variations in the large, AMS Colloq. Publ. vol. 18, AMSProvidence, R. I., 1934. Zbl0011.02802
  15. A. Pazy; [1] Asymptotic expansions of solutions of ordinary differential equations in Hilbert Space, Archive Rat. Mech. Anal.24 (1967), 193-218. Zbl0147.12303MR209618
  16. I.E. Segal; [1] Direct formulation of the causality requirements of the S-operator, Phys. Rev.109 (1958), 2191-2198. Zbl0083.43702MR127852
  17. R.S. Strichartz; [1] The Stationary observer problem for □ u = Mu and related equations, Journal Diff. Eq., 9 (1971), 205-223. Zbl0216.12803
  18. B.R. Vainberg; [1] Principles of radiation, limit absorption and limit amplitude in the general theory of partial differential equations, Russian Math. Surveys, No. 3, 21 (1966), 115-193. Zbl0172.13703MR213701
  19. C.H. Wilcox; [1] A generalization of theorems of Rellich and Atkinson, Proc. AMS.7 (1956), 271-276. Zbl0074.08102MR78912

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