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Continuous dependence for \(2 \times 2\) conservation laws with boundary. (English) Zbl 0884.35091
The author deals with the strictly hyperbolic \(2\times 2\) system of conservation laws \(u_t=F(u)_x=0\) on the domain \(t>0\), \(x>g(t)\) with initial data \(u(0,x)=u_0(x)\) and boundary condition along \(x=g(t)\). Two different kinds of such a boundary condition are investigated: the characteristic \((u(t,g(t))=h(t))\) and the non-characteristic one. Sufficiently small data are considered. For both cases of boundary conditions a Lipschitzian flow is constructed whose trajectories are weak solutions of the problem. Consequently it is proved the continuous dependence of the solution upon the initial data, the boundary condition, and the boundary profile.
Reviewer: A.Doktor (Praha)

MSC:
35L65 Hyperbolic conservation laws
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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