Global solvability of one degenerate semilinear differential operator equation
Global solvability of one degenerate semilinear differential operator equation
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一类简并半线性微分算子方程的全局可解性
DOI：
10.1007/s11072-005-0020-z
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发表时间：
2004
影响因子：
--
通讯作者：
I. G. Khudoshin
中科院分区：
文献类型：
--
作者：
A. Rutkas;I. G. Khudoshin
考虑抽象半线性微分方程的Cauchy问题
$$\frac{d}{{dt}}\left（{Au\left（t \right）} \right）+ Bu\left（t \right）= f\left（{t，u\left（t \right）} \right），t_0- T < t < t_0 + T$$
其中A和B是从Banach空间X到Banach空间Y的线性闭退化算子，f（t，u）是连续可微函数.我们假设预解式（A + μB）−1在点μ = 0处有一个至多二阶的极点。得到了Cauchy问题解的存在唯一性的整体条件。结果被应用到一个非线性退化的偏导数的初边值问题和一个系统的微分代数方程的非线性电路。
AbstractWe consider the Cauchy problem for the abstract semilinear differential equation
$$\frac{d}{{dt}}\left( {Au\left( t \right)} \right) + Bu\left( t \right) = f\left( {t,u\left( t \right)} \right),t_0 - T < t < t_0 + T$$
where A and B are linear closed, generally speaking, degenerate operators acting from a Banach space X into a Banach space Y and f(t, u) is a continuously differentiable function. We assume that the resolvent (A + μB)−1 has a pole of at most second order at the point μ = 0. Global conditions for the existence and uniqueness of a solution of the Cauchy problem are obtained. The results are applied to a nonlinear degenerate initial boundary-value problem with partial derivatives and to a system of differential-algebraic equations of a nonlinear electric circuit.