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BV solutions for the Cauchy problem of a quasilinear hyperbolic equation with $$\sigma$$-finite Borel measure and nonlinear source. (English) Zbl 1077.35085
Summary: The aim of this paper is to discuss the Cauchy problem of the quasilinear hyperbolic equation of the form $$u_{t}+(u^{m})_{x}=u^{p}$$ with nonnegative $$\sigma$$-finite Borel measures as initial conditions, where $$m > 1$$, $$0<p\leqslant 1$$ are some given real numbers. In particular, the existence of BV solutions for the above problem is obtained.
##### MSC:
 35L60 First-order nonlinear hyperbolic equations 35L45 Initial value problems for first-order hyperbolic systems 35R05 PDEs with low regular coefficients and/or low regular data 35D05 Existence of generalized solutions of PDE (MSC2000)
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##### References:
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