Cauchy问题解的不唯一性定理

A THEOREM OF NONUNIQUENESS OF SOLUTIONS FOR THE CAUCHY PROBLEM

设P是R^n上常系数m阶齐次线性偏微分算子,m>1,则对于任何给定的正数c、b、ε,下述Cauchy问题 存在非平凡解u。

Let P() be a homogeneous linear Partial differential operator of order m>1 with constant coefficients on R^n, then for any given positive constants c,b,ε,there exists a non-trivial solution u = u(x,t)∈C~∞(R^n×R_+) for the Cauchy problem:such that