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تسجيل مستخدم جديدGlobal behaviors of defocusing semilinear wave equations
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Shiwu Yang
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In this paper, we investigate the global behaviors of solutions to defocusing semilinear wave equations in $mathbb{R}^{1+d}$ with $dgeq 3$. We prove that in the energy space the solution verifies the integrated local energy decay estimates for the full range of energy subcritical and critical power. For the case when $p>1+frac{2}{d-1}$, we derive a uniform weighted energy bound for the solution as well as inverse polynomial decay of the energy flux through hypersurfaces away from the light cone. As a consequence, the solution scatters in the energy space and in the critical Sobolev space for $p$ with an improved lower bound. This in particular extends the existing scattering results to higher dimensions without spherical symmetry.
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