Variational principles for advection–diffusion problems. (15th March 2018)

• Record Type: Journal Article
• Authors: Auchmuty, Giles
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 6(2018)
• Page Start: 1882
• Page End: 1886
• Publication Date: 2018-03-15
• Subjects: Advection–diffusion equations -- Mixed boundary conditions -- Variational principles; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.09.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Variational principles for linear and semilinear advection–diffusion problems with velocity field given by potential flow are described and analyzed. Mixed Dirichlet and prescribed flux conditions are treated. Existence and uniqueness results are proved and equivalent integral operator equations are found. A positive multiplier function related to the potential of the flow is used to change the system to divergence form. The dependence of the solution on inhomogeneous flux boundary data is determined.