Existence, global nonexistence, and asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized damped Boussinesq-type equation
نویسندگان
چکیده
where u (x, t) denotes the unknown function, f (s) is the given nonlinear function, u0 (x) and u1 (x) are the given initial value functions, k is a constant, the subscript t indicates the partial derivative with respect to t, n is the dimension of space variable x, and △ denotes the Laplace operator in R. The effects of small nonlinearity and dispersion are taken into consideration in the derivation of Boussinesq equations, but in many real situations, damping effects are compared in strength to the nonlinear and dispersive ones. Therefore, the damped Boussinesq equation is considered as well:
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