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Existence and Uniqueness of a Solution to the Cauchy Problem for the Damped Boussinesq Equation

✍ Scribed by V. Varlamov

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
499 KB
Volume
19
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by G. F. Roach

We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t > 0 on a bounded time interval.

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