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$% F. Caetano, On the existence of weak solutions to the Cauchy problem for a class of quasilinear hyperbolic equations with a source term, Rev. Mat. Complut. 17 (2004), 147–167.%$

On the Existence of Weak Solutions to the Cauchy Problem for a Class of Quasilinear Hyperbolic Equations with a Source Term

Filipa CAETANO
Dep. Matemática,
Universidade Nova de Lisboa and CMAF/UL,
Faculdade de Ciências e Tecnologia,
Quinta da Torre, Monte da Caparica,
2829-516 Caparica — Portugal
fmc@fct.unl.pt

Received: January 10, 2002
Accepted: October 2, 2003
ABSTRACT

Following the ideas of D. Serre and J. Shearer (1993), we prove in this paper the existence of a weak solution of the Cauchy problem for the second order quasilinear hyperbolic equation

' ftt-s (fx)fxx+ F (f) =0, (x,t) (- R× [0,+o o [,

where F(f) is a suitable source term.

Key words: Quasilinear hyperbolic equations, conservation laws, viscosity approximation, compensated compactness, Young measures.
2000 Mathematics Subject Classification: Primary: 35L70; Secondary: 35L45.