On linear hyperbolic systems with multiple characteristics. (English) Zbl 0822.47043

Hieber, Matthias

Differ. Integral Equ. 8, No. 4, 877-886 (1995).

Summary: The \(L^ p\) behavior of systems of linear, hyperbolic partial differential equations is examined by means of the theory of integrated semigroups. We show in particular how the degree of integration and therefore the regularity of the solution depends on the multiplicity of the eigenvalues of the symbol.

MSC:

47D06	One-parameter semigroups and linear evolution equations
34G10	Linear differential equations in abstract spaces

Keywords:

\(L^ p\) behavior of systems of linear, hyperbolic partial differential equations; integrated semigroups; degree of integration; regularity of the solution; multiplicity of the eigenvalues of the symbol