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We consider the existence, both locally and globally in time, the asymptotic behaviour, and the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative and dispersive terms. Under rather mild conditions on the nonlinear term and the initial data we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the solution decays exponentially to zero as t →+∞. Finally, under a suitable condition on the nonlinear term, we prove that the local solutions with negative and nonnegative initial energy blow up in finite time.

We consider the blow up of solution to the initial boundary value problem for the generalized Boussinesq equation with damping term. Under some assumptions we prove that the solution with negative initial energy blows up in finite time

We consider the blow-up of solutions as a function of time to the initial boundary value problem for the damped Boussinesq equation. Under some assumptions we prove that the solutions with vanishing initial energy blow up in finite time

We consider a coupled system of viscous Burgers' equations with appropriate initial values using the decomposition method. In this method, the solution is calculated in the form of a convergent power series with easily computable components. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The decomposition series solution of the problem is quickly obtained by observing the existence of the self-canceling “noise” terms where the sum of components vanishes in the limit.

By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components. The decomposition series analytic solution of the problem is quickly obtained by observing the existence of the self-canceling “noise” terms where sum of components vanishes in the limit.

We consider a coupled system of viscous Burgers' equations with appropriate initial values using the decomposition method. In this method, the solution is calculated in the form of a convergent power series with easily computable components. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The decomposition series solution of the problem is quickly obtained by observing the existence of the self-canceling “noise” terms where the sum of components vanishes in the limit.

By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components. The decomposition series analytic solution of the problem is quickly obtained by observing the existence of the self-canceling “noise” terms where sum of components vanishes in the limit.