19 Characteristics. Invariant Form of the Cauchy–Kovalevska Theorem
1975; Elsevier BV; Linguagem: Inglês
10.1016/s0079-8169(08)61522-6
ISSN2162-3481
Tópico(s)Elasticity and Wave Propagation
ResumoPublisher SummaryThe chapter presents a discussion on the characteristics of the invariant form of the Cauchy-Kovalevska theorem. The chapter discusses an equation that is restricted to the scalar case—that is, where the coefficients are complex-valued. The general case of systems is more difficult to analyze. The chapter includes a definition which states the function Pm (y, η) on Ҫ × RN is called “the principal symbol of the differential operator P(y, Dy).” The hypersurface S ∈ Ҫ is said to be characteristic at the point y ∈ S with respect to P(y, Dy) if any normal covector η to S at the point y is characteristic with respect to P(y, Dy) at that point—that is, belongs to Cp(y).
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