On the existence of weak solutions to the Cauchy problem for a class of quasilinear hyperbolic equations with a source term.

摘要

Following the ideas of D. Serre and J. Shearer in [16], we prove in this paper the existence of a weak solution of the Cauchy problem for the second order quasilinear hyperbolic equation Φtt − σ'(Φx) Φ xx + F(Φ) = 0, (x, t) E R x [0,+1[, where F(Φ) is a suitable source term.