发表机构
Institute of Mathematics, University of Silesia in Katowice（卡托维兹西里西亚大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用常数变易公式，在光滑线性算子和有限非线性项作用下求解半线性发展方程，确定初始条件容许空间，分析解的性质，并应用于修正粘性Cahn-Hilliard方程、细胞群体演化及半线性Schrödinger方程。
AI 中文摘要
通过光滑线性算子的作用和一族给定Banach空间中有限多个非线性项，利用常数变易公式求解半线性发展方程。确定了初始条件的容许空间，以保证适当意义下解的存在唯一性。分析了其最大存在时间、短时和爆破时间轮廓、全局可延拓性及正则性。对于Banach空间的外推分数幂尺度，证明了相应Cauchy问题的可解性。给出了在R^N中修正粘性Cahn-Hilliard方程、不同基因型细胞群体演化以及半线性Schrödinger方程中的应用实例。
英文摘要
Semilinear evolution equations are solved by means of the variation of constants formula under the action of smoothing linear operators and a finite number of nonlinearities operating between chosen Banach spaces of a given family. Admissible spaces of initial conditions are determined for the existence and uniqueness of a suitable notion of solution. Its maximal time of existence, short time and blow up time profiles, global extendibility and regularity are analyzed. For extrapolated fractional power scale of Banach spaces the fulfillment of the corresponding Cauchy problem is shown. Chosen applications to the modified viscous Cahn-Hilliard equation in R^N, the evolution of cell population of varying genotype and the semilinear Schrödinger equation are presented.
Comments35 pages
