Physics – Mathematical Physics
Scientific paper
2005-10-19
Physics
Mathematical Physics
Scientific paper
10.1007/s00220-006-0099-9
The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic PDEs with variable coefficients emerging in a class of the free-boundary problems for viscous flows in non-homogeneous media. Such flows posses an infinite number of conservation laws, whose special cases may be viewed as quadrature identities for solutions of variable-coefficient elliptic PDEs. If such PDEs are gauge equivalent to the Laplace equation (gauge-trivial case), a time-dependent conformal map technique, employed for description of the quadrature domains, leads to differential equations, known as "string" constraints in the theory of integrable systems. Although analogs of the string constraints have non-local forms for gauge-non-trivial equations, it is still possible to construct the quadrature domains explicitly, if the elliptic operator belongs to a class of the Calogero-Moser Hamiltonians.
No associations
LandOfFree
The Variable Coefficient Hele-Shaw Problem, Integrability and Quadrature Identities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Variable Coefficient Hele-Shaw Problem, Integrability and Quadrature Identities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Variable Coefficient Hele-Shaw Problem, Integrability and Quadrature Identities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-242134