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Kamotskii, I. V.; Ruzhanskii, M. V.

Estimates and spectral asymptotics for systems with multiplicities. (English. Russian original) Zbl 1114.35033

Funct. Anal. Appl. 39, No. 4, 308-310 (2005); translation from Funkts. Anal. Prilozh. 39, No. 4, 78-80 (2005).
Summary: We consider elliptic and hyperbolic systems with diagonalizable principal part. Characteristics are allowed to have variable multiplicities. Assuming that the characteristics are generic, we give estimates for solutions of a hyperbolic Cauchy problem in \(L^p\) spaces. The first and second terms of the spectral asymptotics are obtained for the corresponding elliptic system.

Cited in 2 Documents

MSC:

35B45 A priori estimates in context of PDEs
35J45 Systems of elliptic equations, general (MSC2000)
35L55 Higher-order hyperbolic systems

Keywords:

Fourier integral operator; elliptic systems; hyperbolic systems; diagonalizable principal part; Cauchy problem
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References:

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