二阶线性发展方程初值问题的某些推广

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Some Extensions of the Initial Value Problem for Second Order Evolution Equations

摘要: 本文用压缩半群理论讨论了二阶线性发展方程组的初值问题;还用解析半群讨论了一类变系数的二阶线性发展方程的初值问题,使这一类初值问题的可解性与含t的算子的一阶线性发展方程解的理论统一起来,这是数学力学中的一类重要方程。

Abstract: The initial problem for second order linear evolution equation systems is discussed by using the contraction semigroup theory. A kind of initial value problem for second order is also discussed with variable coefficients for evolution equations by using the analytical semigroup theory, and is unified with the solutions of the initial value problem for this class of equations and those of first order temporally inhomogeneous evolution equations. This is an important class of equations in mathematical mechanics.

[1]	Showalter, R.E., Hilbert Space Methods for Partial Differential Equations, Pitman London(1977).
[2]	Tanabe, H., Remarks on the equations of evolutions in a Banach space, Osaka Math.J.12(1960).
[3]	Nie Yi-yi(聂仪一), Anti-symmetric system of 2nd order evolution equations, Acta Mathematica Scientia, 4, (1984).