Strongly Hyperbolic Systems with Variable Coefficients | Zendy

Kunihiko Kajitani | Zendy

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Strongly Hyperbolic Systems with Variable Coefficients

Author(s) -

Kunihiko Kajitani

Publication year - 1973

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195192444

Subject(s) - differentiable function , mathematics , multiplicity (mathematics) , initial value problem , order (exchange) , cauchy distribution , pure mathematics , combinatorics , mathematical analysis , finance , economics

where Aj(x, t) and B(x, t) are matrices of order m, infinitely differentiable with respect to t and x = (xl9...9 xp), and u and / are vector-valued functions with m components. We consider the Cauchy problem for this equation with intial values given at t = tQ>0. We say that the Cauchy problem for (1.1) is uniformly well posed, if for any /(#, t) infinitely differentiable and for any intial value u(x, t0) infinitely differentiable, there exists uniquely the infinitely differentiable solution u(x9 t} of (1.1) in @(XQ, t0, e) = {(#, 0; \ X X Q \ gU0(*o + -0» *o^*^*o + e} for Y » 0

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