Global and almost global existence of small solutions to a dissipative wave equation in 3D with nearly null nonlinear terms
Boyan Jonov Thomas C. Sideris
Communications on Pure & Applied Analysis 2015, 14(4): 1407-1442 doi: 10.3934/cpaa.2015.14.1407
The existence of global small $\mathcal O(\varepsilon )$ solutions to quadratically nonlinear wave equations in three space dimensions under the null condition is shown to be stable under the simultaneous addition of small $\mathcal O(\nu)$ viscous dissipation and $\mathcal O(\delta)$ non-null quadratic nonlinearities, provided that $\varepsilon \delta/\nu\ll 1$. When this condition is not met, small solutions exist ``almost globally'', and in certain parameter ranges, the addition of dissipation enhances the lifespan.
keywords: global existence null condition. Nonlinear dissipative wave equation

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