Short-time asymptotic expansions of semilinear evolution equations

• Published in: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 146; no. 1; pp. 141 - 167
• Main Author: Fahrenwaldt, Matthias A.
• Format: Journal Article
• Language: English
• Published: Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.02.2016; Cambridge University Press
• Subjects: Algebra; Approximation; Asymptotic expansions; Construction; Differential equations; Evolution; Linear equations; Mathematical analysis; Mathematics; Perturbation methods; asymptotic analysis; backward stochastic differential equations; semilinear equations; Banach algebras; Secondary 35B40; Primary 35K58

We develop an algebraic approach to constructing short-time asymptotic expansions of solutions of a class of abstract semilinear evolution equations. The expansions are typically valid for both the solution of the equation and its gradient. We apply a perturbation approach based on the symbolic calc...