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