Mathematics – Analysis of PDEs
Scientific paper
2009-08-15
Mathematics
Analysis of PDEs
27 pages, 4 figures
Scientific paper
We consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain distributions of any order of singularity. It is known that such problems have a unique continuous solution if the initial data are continuous. In the case of strongly singular initial data we prove the existence of a (unique) delta wave solution. In both cases, we say that a solution is smoothing if it eventually becomes $k$-times continuously differentiable for each $k$. Our main result is a criterion allowing us to determine whether or not the solution is smoothing. In particular, we prove a rather general smoothingness result in the case of classical boundary conditions.
No associations
LandOfFree
Smoothing Solutions to Initial-Boundary Problems for First-Order Hyperbolic Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Smoothing Solutions to Initial-Boundary Problems for First-Order Hyperbolic Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Smoothing Solutions to Initial-Boundary Problems for First-Order Hyperbolic Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-76197