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Some uniqueness and growth theorems in the Cauchy problem for \(Pu_{tt}+Mu_t+Nu=0\) in Hilbert space. (English) Zbl 0238.35016


MSC:

35G10 Initial value problems for linear higher-order PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B45 A priori estimates in context of PDEs
47F05 General theory of partial differential operators
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References:

[1] Agmon, S.: Unicité et convexité dans les problèmes différentiels. Sem. Math. Sup. (1965), Univ. of Montreal Press (1966).
[2] John, F.: Continuous dependence on data for solutions of partial differential equations with a prescribed bound. Commun. Pure Appl. Math.13, 551-585 (1960). · Zbl 0097.08101 · doi:10.1002/cpa.3160130402
[3] Levine, H.A.: Logarithmic convexity and the Cauchy problem forP(t)u tt +M(t)u t +N(t)u=0 in Hilbert space. Battelle (Geneva) Adv. Studies Centre, Report 49, Sept. 1971.
[4] Levine, H.A.: On the uniqueness of bounded solutions tou?(t)=A(t)u(t) andu?(t)=A(t)u(t) in Hilbert space. SIAM J. on Analysis (In Print). · Zbl 0226.34056
[5] Murray, A.C.: Asymptotic behavior of solutions of hyperbolic inequalities. Trans. Amer. Math. Soc.157, 279-296 (1971). · Zbl 0214.10403 · doi:10.1090/S0002-9947-1971-0274922-5
[6] Ogawa, H.: Lower bounds for solutions of hyperbolic inequalities. Proc. Amer. Math. Soc.16, 853-857 (1965). · Zbl 0138.34804 · doi:10.1090/S0002-9939-1965-0193376-3
[7] Protter, M.H.: Asymptotic behavior and uniqueness theorem for hyperbolic equations and inequalities. Proc. of U.S.-U.S.S.R., Symposium on partial differential equations Novosibirsk (1963), 348-353.
[8] Zaidman, S.: Uniqueness of bounded solutions for some abstract differential equations. Ann. Univ. Ferrara, Sez. VII (N. S.)14, 101-104 (1969). · Zbl 0218.34059
[9] Love, A.E.H.: A freatise on the mathematical theory of Elasticity. Dover, 1944. · Zbl 0063.03651
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