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.
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 problemReferences:
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