SUPERCRITICAL SEMILINEAR WAVE EQUATION WITH NON-NEGATIVE POTENTIAL
SUPERCRITICAL SEMILINEAR WAVE EQUATION WITH NON-NEGATIVE POTENTIAL
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DOI：
10.1081/pde-100107822
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发表时间：
2001-11
影响因子：
1.9
通讯作者：
V. Georgiev;C. Heiming;H. Kubo
中科院分区：
文献类型：
--
作者：
V. Georgiev;C. Heiming;H. Kubo
我们证明了具有光滑正时无关势的线性波动方程解的加权L∞估计。该证明基于摄动拉普拉斯算子的广义傅里叶变换的应用和有限相关域参数。我们利用这一估计证明了具有势的超临界半线性波动方程整体小数据解的存在性。
We prove a weighted L ∞ estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.