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Some remarks on the local energy decay of solutions of the initial- boundary value problem for the wave equation in unbounded domains. (English) Zbl 0337.35046


MSC:

35L05 Wave equation
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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[1] Bers, L; John, F; Schechter, M, Partial differential equations, ()
[2] Lax, P.D; Morawetz, C.S; Phillips, R.S, Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle, Comm. pure appl. math., 16, 477-486, (1963) · Zbl 0161.08001
[3] Lax, P.D; Phillips, R.S, The wave equation in exterior domains, Bull. amer. math. soc., 68, 47-49, (1962) · Zbl 0103.06401
[4] Lax, P.D; Phillips, R.S, Scattering theory, () · Zbl 0117.09104
[5] Morawetz, C.S, The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. pure appl. math., 15, 561-568, (1961) · Zbl 0101.07701
[6] Morawetz, C.S, The limiting amplitude principle, Comm. pure appl. math., 15, 349-361, (1962) · Zbl 0196.41202
[7] Ralston, J.V, Solutions of the wave equation with localized energy, Comm. pure appl. math., 22, 807-823, (1969) · Zbl 0209.40402
[8] Zachmanoglou, E.C, The decay of solutions of the initial-boundary value problem for the wave equation in unbounded regions, Arch. rat. mech. anal., 14, 312-325, (1963) · Zbl 0168.08002
[9] Zachmanoglou, E.C, An example of slow decay of the solution of the initial-boundary value problem for the wave equation in unbounded regions, Bull. amer. math. soc., 70, 633-636, (1964) · Zbl 0127.31704
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