On travelling-wave solutions for a moving boundary problem of Hele-Shaw type

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 74, Issue 1, 2009, Pages 107-127

  Günther, Matthias ^a   Prokert, Georg ^b  

^a UNIVERSITY OF LEIPZIG   (Germany)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Degenerate transport equation; Electrical streamer discharges; Hele Shaw flow; Kinetic undercooling; Moving boundary problem

Indexed keywords

CHANNEL FLOW; DIFFERENTIAL EQUATIONS; KINETIC THEORY; LINEARIZATION; UNDERCOOLING;

DEGENERATE TRANSPORT EQUATION; ELECTRICAL STREAMER DISCHARGES; HELE-SHAW FLOW; KINETIC UNDERCOOLING; MOVING BOUNDARY PROBLEM;

MATHEMATICAL OPERATORS;

EID: 59549087204     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxn029     Document Type: Article

References (12)

1. ARRAYAS, M. & EBERT, U. (2004) Stability of negative ionization fronts: Regularization by electric screening? Phys. Rev. E, 69 36214.
2. EBERT, U., MEULENBROEK, M. & SCHÄFER, L. (2007) Convective stabilization of a Laplacian moving boundary problem with kinetic undercooling. SIAM J. Appl. Math., 68, 292-310.
3. ELSCHNER, J. (1985) Singular Ordinary Differential Operators and Pseudodifferential Equations. Lecture Notes in Mathematics, vol. 1128. Berlin: Springer.
4. GÜNTHER, M. & PROKERT, G. (2005) On a Hele-Shaw-type domain evolution with convected surface energy density. SIAM J. Math. Anal. 37, 372-410.
5. HENRY, D. (2005) Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations. Cambridge: Cambridge University Press.
6. HOWISON, S. D. (1992) Complex variable methods in Hele-Shaw moving boundary problems. Eur. J. Appl. Math., 3, 209-224.
7. KATO, T. (1984) Locally coercive nonlinear equations, with applications to some periodic solutions. Duke Math. J., 51, 923-936.
8. MEULENBROEK, B. (2006) Streamer branching: Conformal mapping and regularization. Ph.D. Thesis, Technische Universiteit Eindhoven, Eindhoven.
9. MEULENBROEK, B., EBERT, U. & SCHÄFER, L. (2005) Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition: Exact results. Phys. Rev. Lett., 95, 195004.
10. PROKERT, G. (1999) Hyperbolic evolution equations for moving boundary problems. Eur. J. Appl. Math., 10, 607-622.
11. ROMERO, L. A. (1981) The fingering problem in a Hele-Shaw cell. Ph.D. Thesis, California Institute of Technology, Pasadena.
12. WLADIMIROW, W. S. (1972) Gleichungen der mathematischen Physik Berlin: Deutscher Verlag der Wissenschaften.