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Abstract: We consider initial-boundary problems for general linear first-order strictlyhyperbolic systems with local or nonlocal nonlinear boundary conditions. Whileboundary data are supposed to be smooth, initial conditions can containdistributions of any order of singularity. It is known that such problems havea unique continuous solution if the initial data are continuous. In the case ofstrongly singular initial data we prove the existence of a unique delta wavesolution. In both cases, we say that a solution is smoothing if it eventuallybecomes $k$-times continuously differentiable for each $k$. Our main result isa criterion allowing us to determine whether or not the solution is smoothing.In particular, we prove a rather general smoothingness result in the case ofclassical boundary conditions.



Author: Irina Kmit

Source: https://arxiv.org/



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