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Smooth approximations of global in time solutions to scalar conservation laws. (English) Zbl 1172.35450

Summary: We construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. Different kinds of singularities interactions which arise during the evolution of the initial data are described as well. In order to solve the problem, we use and further develop the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.

MSC:

35L65 Hyperbolic conservation laws
35A35 Theoretical approximation in context of PDEs
35L45 Initial value problems for first-order hyperbolic systems
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