科研之友
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摘要
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 solutions and distributional solutions is established. Moreover, the propagation of singularities is studied.
