Applied Analysis

The department is a leader in the analysis of systems of nonlinear differential equations that arise in modeling a variety of physical phenomena. They include problems in biology, chemistry, phase transitions, fluid flow, flame propagation, diffusion processes, and pattern formation in nonlinear stochastic partial differential equations. Research in these areas is aided by a variety of computational facilities, including Sun Microsystem work stations and the massively parallel machines at the Pittsburgh Supercomputing Center.

Applied analysis is an important area of research in the Department of Mathematics.


Conservation Laws
Wang's research area is nonlinear partial differential equations and applied mathematics.
Free Boundary Problems in Mathematical Finance
Chadam's recent research efforts have been focused on the study of free boundary problems that arise in mathematical finance. With his colleague, Xinfu Chen, their students, and foreign collaborators, he has studied early exercise boundaries for Amer
Lattice Models of Phase Transitions in Crystalline Solids
Vainchtein's research program seeks to advance the understanding of the dynamics of phase transitions in crystalline solids from the perspective of mesoscopic and microscopic frameworks.
Nonlinear Analysis, Partial Differential Equations and Calculus of Variations.
Lewicka's research areas are nonlinear analysis, partial differential equations and calculus of variations. She has obtained results on the well-posedness and stability of systems of conservation laws and reaction-diffusion equations.
Nonlinear Differential Equations
Chen studies a wide variety of problems on such topics such as non-linear partial differential equations of parabolic and elliptic type, ordinary differential equations and dynamical systems, free boundary problems and interfacial dynamics, singular
Pattern Formation in Coupled Cell Networks
The general topic of Rubin's research is spatio-temporal pattern formation in coupled cell networks. The overall goal of this research is to understand how the intrinsic dynamics of network elements interact with the architecture and properties of co
Pattern Formation in Wilson-Cowan Networks
The general topic of Troy's research is spatio-temporal pattern formation in coupled Wilson-Cowan networks.
Phase Field Equations; Renormalization and Scaling in Differential Equations
Prof. Caginalp and collaborators developed many aspects of the phase field equations that describe interfaces using a smooth transition.

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The Dietrich School of
Arts and Sciences
301 Thackeray Hall
Pittsburgh, PA 15260
Phone: 412-624-8375
Fax: 412-624-8397


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