Methods and Applications of Analysis

Volume 20 (2013)

Number 3

Semigroup-theoretical approach to higher order nonlinear evolution equations

Pages: 237 – 260

DOI: http://dx.doi.org/10.4310/MAA.2013.v20.n3.a2

Authors

Qianshun Chang (Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing, China)

Tujin Kim (Institute of Mathematics, Academy of Sciences, Pyongyang, Korea)

Jing Xu (School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China)

Abstract

We are concerned with application of the semigroup theory to the higher order nonlinear evolution equations. First, we show some necessary conditions for the accretivity of matrices of nonlinear operators in Banach spaces in relation to the underlying phase spaces and domains of operators. Then, we obtain a condition for a matrix of linear operators to generate an analytic semigroup. These results are, finally, applied to Cauchy problems of nonlinear and quasilinear evolution equations of higher order.

Keywords

accretivity of operator matrices, analytic semigroup, nonlinear higher order evolution equation, pseudo-hyperbolic system

2010 Mathematics Subject Classification

34G20, 35L82, 47D03, 47H20

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