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Volume 2, Issue 1
Estimation for Solutions of Ill-Posed Cauchy Problems of Differential Equation with Pseudo-Differential Operators

Guan-Quan Zhang

J. Comp. Math., 2 (1984), pp. 10-23.

Published online: 1984-02

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  • Abstract

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.

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@Article{JCM-2-10, author = {Guan-Quan Zhang}, title = {Estimation for Solutions of Ill-Posed Cauchy Problems of Differential Equation with Pseudo-Differential Operators}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {1}, pages = {10--23}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9635.html} }
TY - JOUR T1 - Estimation for Solutions of Ill-Posed Cauchy Problems of Differential Equation with Pseudo-Differential Operators AU - Guan-Quan Zhang 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.

Guan-Quan Zhang. (1984). Estimation for Solutions of Ill-Posed Cauchy Problems of Differential Equation with Pseudo-Differential Operators. Journal of Computational Mathematics. 2 (1). 10-23. doi:
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