Hilbert空间中的二阶线性发展方程

本文应用K-T-阶发展方程理论讨论Hilbert空间中形如 (*)的二阶线性发展方程解的存在唯一性及(*)中各项依各自范数对t的连续性,作为准备,本文证明了:若A(t)是由某种拟双线性型导出,则有从而证明一阶发展方程解的一阶导数在初始点t=O连续,在t>O解有二阶导数,由此给出(*)解的存在唯一性和(*)中各项依各自范数对t连续的条件。     

Some extensions of the initial value problem for second order evolution equations

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.     

半线性方程的边值问题

§1.引言本文考虑如下退化的椭圆方程的边值问题:     

SOME EXTENSIONS OF THE INITIAL VALUE PROBLEM FOR SECOND ORDER EVOLUTION EQUATIONS

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

二阶线性发展方程初值问题的某些推广

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。