一类带非线性源的拟线性双曲方程以测度为初值的BV解

BV Solutions for a Class of Quasilinear Hyperbolic Equations with Nonlinear Source and Measures as Initial Conditions

讨论拟线性双曲方程ut+(um)x=tqup,以σ-有限的Borel测度为初值的Cauchy问题,其中m>1,0<p≤1,q≥0是给定常数,证明了BV解的存在性.

The aim of the present paper is to discuss the Cauchy problem for a class of quasilinear hyper- bolic equations of the form ut＋（u^m）x=t^qu^p with σ- finite Borel measures as initial conditions, where m〉1,0〈P≤1,q≥0 are some given real numbers,the existence of BV solutions for the above problem is obtained.