Energy splitting
Authors:
David G. Costa and Walter A. Strauss
Journal:
Quart. Appl. Math. 39 (1981), 351-361
MSC:
Primary 35L45; Secondary 78A25, 81C05, 81E10
DOI:
https://doi.org/10.1090/qam/636240
MathSciNet review:
636240
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Additional Information
- G. S. S. Ávila and D. G. Costa, Asymptotic properties of general symmetric hyperbolic systems, J. Functional Analysis 35 (1980), no. 1, 49–63. MR 560217, DOI https://doi.org/10.1016/0022-1236%2880%2990080-4
- C. Bardos and D. G. Costa, Decay along non-bicharacteristic rays of solutions of first order hyperbolic systems, J. Math. Pures Appl. (9) 53 (1974), 427–437. MR 374687
- A. R. Brodsky, On the asymptotic behavior of solutions of the wave equations, Proc. Amer. Math. Soc. 18 (1967), 207–208. MR 212417, DOI https://doi.org/10.1090/S0002-9939-1967-0212417-X
- David Goldstein Costa, On partition of energy for uniformly propagative systems, J. Math. Anal. Appl. 58 (1977), no. 1, 56–62. MR 470505, DOI https://doi.org/10.1016/0022-247X%2877%2990227-X
D. G. Costa and W. A. Strauss, Energy asymptotics of hyperbolic systems, A.M.S. Notices 26, A-434 (1979)
G. Dassios, Equipartition of energy for Maxwell’s equations, Quart. Appl. Math. (to appear)
- George Dassios, Equipartition of energy in elastic wave propagation, Mech. Res. Comm. 6 (1979), no. 1, 45–50. MR 524233, DOI https://doi.org/10.1016/0093-6413%2879%2990078-8
- George Dassios and Efstratios Galanis, Asymptotic equipartition of kinetic and strain energy for elastic waves in anisotropic media, Quart. Appl. Math. 38 (1980/81), no. 1, 121–128. MR 575835, DOI https://doi.org/10.1090/S0033-569X-1980-0575835-4
- F. G. Friedlander, On the radiation field of pulse solutions of the wave equation. II, Proc. Roy. Soc. London Ser. A 279 (1964), 386–394. MR 164132, DOI https://doi.org/10.1098/rspa.1964.0111
- R. T. Glassey and W. A. Strauss, Decay of classical Yang-Mills fields, Comm. Math. Phys. 65 (1979), no. 1, 1–13. MR 526974
C. Huygens, Traité de la Lumière, Paris, 1690
- Fritz John, Plane waves and spherical means applied to partial differential equations, Interscience Publishers, New York-London, 1955. MR 0075429
- Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
- P. D. Lax and R. S. Phillips, Decaying modes for the wave equation in the exterior of an obstacle, Comm. Pure Appl. Math. 22 (1969), 737–787. MR 254432, DOI https://doi.org/10.1002/cpa.3160220603
- P. D. Lax and R. S. Phillips, Scattering theory for the acoustic equation in an even number of space dimensions, Indiana Univ. Math. J. 22 (1972/73), 101–134. MR 304882, DOI https://doi.org/10.1512/iumj.1972.22.22011
- Walter A. Strauss, Decay and asymptotics for $ cmu=F(u)$, J. Functional Analysis 2 (1968), 409–457. MR 0233062, DOI https://doi.org/10.1016/0022-1236%2868%2990004-9
- Walter A. Strauss, The existence of the scattering operator for moving obstacles, J. Functional Analysis 31 (1979), no. 2, 255–262. MR 525956, DOI https://doi.org/10.1016/0022-1236%2879%2990066-1
W. A. Strauss, Some energy components tend to zero globally, A.M.S. Notices 26, A-431 (1979)
- Robert S. Strichartz, Asymptotic behavior of waves, J. Functional Analysis 40 (1981), no. 3, 341–357. MR 611588, DOI https://doi.org/10.1016/0022-1236%2881%2990053-7
- Calvin H. Wilcox, Scattering theory for the d’Alembert equation in exterior domains, Lecture Notes in Mathematics, Vol. 442, Springer-Verlag, Berlin-New York, 1975. MR 0460927
- Calvin H. Wilcox, Asymptotic wave functions and energy distributions in strongly propagative anisotropic media, J. Math. Pures Appl. (9) 57 (1978), no. 3, 275–321. MR 513101
G. S. S. Avila and D. G. Costa, Asymptotic properties of general symmetric hyperbolic systems, J. Funct. Anal. (to appear)
C. Bardos and D. G. Costa, Decay along nonbicharacteristic rays of solutions of the first-order hyperbolic systems, J. Math. Pures Appl. 53, 427–435 (1974)
A. R. Brodsky, On the asymptotic behavior of solutions of the wave equation, Proc. A.M.S. 18, 207–8 (1967)
D. G. Costa, On partition of energy for uniformly propagative systems, J. Math. Anal. App. 58, 56–62 (1977)
D. G. Costa and W. A. Strauss, Energy asymptotics of hyperbolic systems, A.M.S. Notices 26, A-434 (1979)
G. Dassios, Equipartition of energy for Maxwell’s equations, Quart. Appl. Math. (to appear)
G. Dassios. Equipartition of energy in elastic wave propagation, Mech. Res. Comm. 6, 45–50 (1979)
G. Dassios and E. Galanis, Asymptotic equipartition of kinetic and strain energy for elastic waves in anisotropic media, Quart. Appl. Math. 38, 121–128 (1980)
F. G. Friedlander, On the radiation field of pulse solutions of the wave equation II, Proc. Roy. Soc. London 279A, 386–394 (1964)
R. Glassey and W. A. Strauss, Decay of classical Yang-Mills fields, Comm. Math. Phys. 65, 1–13 (1979). Also, Propagation of the energy of Yang-Mills fields, in: Bifurcation phenomena in mathematical physics (ed. D. Bessis and C. Bardos), Reidel Publ. Co. (to appear)
C. Huygens, Traité de la Lumière, Paris, 1690
F. John, Plane waves and spherical means applied to partial differential equations, Interscience, 1955
P. D. Lax and R. S. Phillips, Scattering theory, Academic Press, 1967
P. D. Lax and R. S. Phillips, Decaying modes for the wave equation, Comm. Pure App. Math. 22, 737–787 (1969)
P. D. Lax and R. S. Phillips, Scattering theory for the acoustic equation in an even number of space dimensions, Indiana U. Math. J. 22, 101–134 (1972)
W. A. Strauss, Decay and asymptotics for $u = F\left ( u \right )$, J. Funct. Anal. 2, 409–457 (1968)
W. A. Strauss, Existence of the scattering operator for moving obstacles, J. Funct. Anal. 31, 255–262 (1979)
W. A. Strauss, Some energy components tend to zero globally, A.M.S. Notices 26, A-431 (1979)
R. S. Strichartz, Asymptotic behavior of waves (to appear)
C. H. Wilcox, Scattering theory for the d’Alembert equation in exterior domains, Lecture Notes in Math. No. 442, Springer, 1975
C. H. Wilcox, Asymptotic wave functions and energy distributions in strongly propagative anisotropic media, J. Math. Pures Appl. 57, 275–321 (1978)
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Article copyright:
© Copyright 1981
American Mathematical Society