On the Cauchy Problem for Quasilinear Hyperbolic Systems of Partial Differential-Functional Equations of the First Order | Zendy

Tomasz Człapiński | Zendy

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On the Cauchy Problem for Quasilinear Hyperbolic Systems of Partial Differential-Functional Equations of the First Order

Author(s) -

Tomasz Człapiński

Publication year - 1991

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/439

Subject(s) - hyperbolic partial differential equation , uniqueness , mathematics , cauchy problem , elliptic partial differential equation , initial value problem , mathematical analysis , order (exchange) , cauchy boundary condition , partial differential equation , picard–lindelöf theorem , first order , fixed point theorem , boundary value problem , neumann boundary condition , finance , economics

We denote by R" the n-dimensional real vector space with the norm Its II = max1515lsl (s = s) € R') and by M(m,k) the space of real m x k matrices. Furthermore by C(X,Y) we denote the usual space of continuous functions from Xto Yand by L1(I,R+) the usual space of Lebesgue integrable functions, I C R being an interval and R+ = [0, +co). Let Jbe the set of all functions (P = (p .... . pm) E C([-h, 0] x R T Rm ), h "?: 0, such that, for some A, r € R, and W € L 1 ([-h, 01, R+),

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