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Maximal rates of decay of solutions of partial differential equations. (English) Zbl 0215.45203


MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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[1] Goodman, R., Causal S-operators and domains of dependence for hyperbolic equations. Thesis, M.I.T., 1963.
[2] Goodman, R., One sided invariant subspaces and domains of uniqueness for hyperbolic equations. Proc. A.M.S. 15, 653–660 (1964). · Zbl 0132.35706 · doi:10.1090/S0002-9939-1964-0170119-X
[3] Grušin, V.V., On Sommerfeld type conditions. Mat. Sb. (N.S.) 61 (103), 147–174 (1963). (Russian.)
[4] Lions, J.L., Supports dans la transformation de Laplace. J. Analyse Math. 2, 369–380 (1953). · Zbl 0051.33504 · doi:10.1007/BF02825641
[5] Littman, W., Decay at infinity of solutions to partial differential equations with constant coefficients. Trans. A.M.S. 123, 449–459 (1966). · Zbl 0144.13403 · doi:10.1090/S0002-9947-1966-0197951-7
[6] Masuda, K., On the exponential decay of solutions of some partial differential equations. J. Math. Soc. Japan 19 (1967) · Zbl 0148.34603
[7] Morawetz, C., A uniqueness theorem for the relativistic wave equation. Comm. Pure Appl. Math. 16, 353–362 (1963). · Zbl 0117.06402 · doi:10.1002/cpa.3160160309
[8] Rellich, F., Über das asymptotische Verhalten der Lösungen von 20-01 in unendlichen Gebieten. Jber. Deutsch. Math.-Verein. 53, 57–65 (1943). · Zbl 0028.16401
[9] Segal, I.E., Direct formulation of the causality requirements of the S-operator. Phys. Rev. 109, 2191–2198 (1958). · Zbl 0083.43702 · doi:10.1103/PhysRev.109.2191
[10] Trèves, F., Lectures on partial differential equations with constant coefficients. Notas de Matemática No. 27, Instituto de Matemático Pura e Aplicado, Rio de Janeiro, 1961.
[11] Wilcox, C.H., Steady-state wave propagation in homogeneous anisotropic media. Arch. Rational Mech. Anal. 25, 201–242 (1967). · Zbl 0159.14401 · doi:10.1007/BF00251589
[12] Wolsson, K., A generalization of the Rellich growth theorem. Thesis, New York University, (1962) Unpublished.
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