Interval Cauchy problem with a second type Hukuhara derivative
Interval Cauchy problem with a second type Hukuhara derivative
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DOI：
10.1016/j.ins.2012.05.022
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发表时间：
2012-12
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通讯作者：
M. T. Malinowski
中科院分区：
文献类型：
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作者：
M. T. Malinowski
本文考虑区间微分方程。这样的方程可以适用于参数不确定性存在下的动力系统建模。研究了一类带第二类Hukuhara导数的区间初值问题。通过一个实际应用的例子，我们指出了使用这种区间值导数的优点。一个连续的依赖性的解决方案的初始值和右手边的方程。首先证明了近似局部解的存在性，然后利用该定理证明了具有第二类Hukuhara导数的区间Cauchy问题至少存在一个局部解.并给出了解集的紧性。最后，给出了线性区间微分方程局部解的显式公式。
In this paper we consider interval differential equations. Such the equations can be appropriate in modeling of dynamical systems under presence of uncertainty of parameters. We study an interval initial value problem with a second type Hukuhara derivative. By an example of real-world application we indicate the advantages of the usage of such a kind of interval-valued derivative. A continuous dependence of the solution on initial value and right-hand side of the equation is shown. The existence of approximate local solutions is proven, and then it is used in the derivation of existence of at least one local solution to interval Cauchy problem with second type Hukuhara derivative. The compactness of solutions set is also stated. Finally, the explicit formulae for local solutions to linear interval differential equations are provided.