Methods and Applications of Analysis
Volume 20 (2013)
Semigroup-theoretical approach to higher order nonlinear evolution equations
Pages: 237 – 260
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.
accretivity of operator matrices, analytic semigroup, nonlinear higher order evolution equation, pseudo-hyperbolic system
2010 Mathematics Subject Classification
34G20, 35L82, 47D03, 47H20