TY - JOUR T1 - Estimation for Solutions of Ill-Posed Cauchy Problems of Differential Equation with Pseudo-Differential Operators JO - Journal of Computational Mathematics VL - 1 SP - 10 EP - 23 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9635.html KW - AB -
The estimation for solutions for the ill-posed Cauchy problems of the differential equation $\frac{du(t)}{dt}=A(t)u(t)+N(t)u(t),\forall t\in (0,1)$ is discussed, where $A(t)$ is a 2-nd order p.d.o. and $N(t)$ is a uniformly bounded $h-›H$ linear operator. Two estimates of $||u(t)||$ are obtained.