外区域上四阶半线性波动方程的能量衰减估计

Energy Decay for Semilinear Fourth Order Wave Equations in Exterior Domains

研究外区域Ω上的四阶波动方程utt+Δ2u+ut=f(u)其中非线性项f(u)取为|u|αu,α>0.首先,得到一般外区域上解的能量衰减估计,即边界Ω不加任何几何条件.进而,提高初值的正则性,又得到更好的衰减估计.

The paper considers the fourth order wave equations utt ＋△^2u ＋ut =｜u｜^αu in exterior domains. Energy decay derives in general exterior domain Ω without any geometrical condition imposed on the boundary 偏dΩ. Further, under the improved regularity of the initial data, a better decay results can be obtained.