Weakly hyperbolic equation with fast oscillating coefficients
Weakly hyperbolic equation with fast oscillating coefficients
复制标题
具有快速振荡系数的弱双曲方程
DOI：
10.18910/6891
复制
发表时间：
1999
影响因子：
0.4
通讯作者：
K. Yagdjian
中科院分区：
文献类型：
--
作者：
M. Reissig;K. Yagdjian
（r * 与m无关）如果a（t）仅为“Log-Lipschitz”。这意味着我们失去了规律性。若将a（t）> c > 0弱化为a（t）> 0，则得到一个弱双曲柯西问题.这里a = a（t）的高度正则性不足以证明Sobolev空间中解的存在性。在[2]中，虽然系数a（t）属于C°°（[0，oo）），但系数a（t）的某些振荡行为导致Sobolev空间中解的不存在性结果.有不同的方法来排除这个反例，也就是说，控制振荡的影响。一种方法是为a = a（t）e C^Oj [r]）规定一个非局部条件，
(Γ* is independent of m) if a(t) is only "Log-Lipschitz". This means we have a loss of regularity. If we weaken a(t) > c > 0 to a(t) > 0, then we obtain a weakly hyperbolic Cauchy problem. Here high regularity of a = a(t) is not sufficient for the existence of the solution in Sobolev spaces. In [2] it was shown that some oscillating behaviour of the coefficient a(t) leads to a nonexistence result for the solutions in Sobolev spaces although the coefficient belongs to C°°([0, oo)). There are different ways to exclude this counterexample, that means, to control the influence of the oscillations. One way is to prescribe a nonlocal condition for a = a(t) e C^OjΓ]) of the type