Higher Dimensional SLEP Equation and Applications to Morphological Stability in Polymer Problems

• Published in: SIAM journal on mathematical analysis Vol. 36; no. 3; pp. 916 - 966
• Main Authors: Nishiura, Yasumasa, Suzuki, Hiromasa
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 2005
• Subjects: Exact sciences and technology; Mathematical analysis; Mathematics; Morphology; Partial differential equations; Sciences and techniques of general use; Matched asymptotic expansion; Patterning; Existence of solution; 35B35; Singular perturbation; reaction diffusion system; Eigenvalue; critical eigenvalues 35B25; Stability criterion; Reaction diffusion equation; 35K57; Mathematical analysis; Diblock copolymer; pattern formation; stability

Existence and stability of stationary internal layered solutions to a rescaled diblock copolymer equation are studied in higher dimensional space. Rescaling is necessary since the characteristic domain size of any stable pattern eventually vanishes in an appropriate singular limit. A general suffici...