A linear first-order hyperbolic equation with discontinuous coefficient: distributional shadows and propagation of singularities
It is well-known that distributional solutions to the Cauchy problem for $u_t + (b(t,x)u)_{x} = 0$ with $b(t,x) = 2H(x-t)$, where H is the Heaviside function, are non-unique. However, it has a unique generalized solution in the sense of Colombeau. The relationship between its generalized solutio...
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| Format: | Article |
| Language: | English |
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Texas State University
2011-06-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/76/abstr.html |