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Existence and Uniqueness of a Solution to the Cauchy Problem for the Damped Boussinesq Equation
Author(s) -
Varlamov V.
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960525)19:8<639::aid-mma786>3.0.co;2-c
Subject(s) - uniqueness , mathematics , bounded function , mathematical analysis , initial value problem , cauchy problem , space (punctuation) , differentiable function , cauchy distribution , interval (graph theory) , wave equation , linguistics , philosophy , combinatorics
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.