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| ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM |
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Citation： |
J. P. DIAS,M. FIGUEIRA.ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM[J].Chinese Annals of Mathematics B,2002,23(3):317~324 |
| Page view： 1104
Net amount： 769 |
Authors： |
J. P. DIAS; M. FIGUEIRA |
Foundation： |
Project supported by the FCT and FEDER. |
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| Abstract： |
This paper is a continuation of the authors' previous paper [1]. In this paper the authors prove, assuming additional conditions on the initial data, some results about the existence and uniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolic system
$$ \left\{\matrix\format\l &\quad \l\ a_t + (au)_x + {{2au}\over x} = 0, & \ & x>0,\,\, t\geq 0. \ u_t + {1\over 2}\, (a^2 + u^2)_x = 0, &
\endmatrix\right.
$$ |
Keywords： |
Cauchy problem, Weak solution, Quasilinear hyperbolic system |
Classification： |
35L45, 35L67 |
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