A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions

Florian Mehats; Jean-Michel Roquejoffre

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 6, page 691-724
  • ISSN: 0294-1449

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Mehats, Florian, and Roquejoffre, Jean-Michel. "A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions." Annales de l'I.H.P. Analyse non linéaire 16.6 (1999): 691-724. <http://eudml.org/doc/78480>.

@article{Mehats1999,
author = {Mehats, Florian, Roquejoffre, Jean-Michel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {plasma physics; discontinuities; continuity properties},
language = {eng},
number = {6},
pages = {691-724},
publisher = {Gauthier-Villars},
title = {A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions},
url = {http://eudml.org/doc/78480},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Mehats, Florian
AU - Roquejoffre, Jean-Michel
TI - A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 6
SP - 691
EP - 724
LA - eng
KW - plasma physics; discontinuities; continuity properties
UR - http://eudml.org/doc/78480
ER -

References

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  2. [2] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I and II, Comm. Pure Appl. Math., 12, 1959, pp. 623-727; 17, 1964, pp. 35-92. Zbl0093.10401MR162050
  3. [3] G. Barles, Fully nonlinear Neumann type boundary conditions for second-order elliptic and parabolic equations. J. Diff. Equations, Vol. 106, No. 1, 1993, pp. 90-106.. Zbl0786.35051MR1249178
  4. [4] A. Chuvatin, Thèse de doctorat de l'École polytechnique, 1994. 
  5. [5] M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order Partial differential equations. Bull. Amer. Soc,. 27, 1992, pp. 1-67. Zbl0755.35015MR1118699
  6. [6] L.C. Evans and R. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Math., CRC Press, Ann Arbor, 1992. Zbl0804.28001MR1158660
  7. [7] A.V. Gordeev, A.V. Grechikha and Y.L. Kalda, Rapid penetration of a magnetic field into a plasma along an electrode, Sov. J. Plasma Phys., 16, Vol. 1, 1990, pp. 55-57. 
  8. [8] R.J. Leveque, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhäuser Verlag, 1990. Zbl0723.65067MR1077828
  9. [9] G. Lieberman and N. Trudinger, Nonlinear oblique boundary value problems for nonlinear elliptic equations, Trans. A.M.S, Vol. 295, 1986, pp. 509-546. Zbl0619.35047MR833695
  10. [10] P.-L. Lions and P.E. Souganidis, Convergence of MUSCL type methods for scalar conservation laws, C.R. Acad. Sci. Paris, Vol. 311, 1990, Série I, pp. 259-264. Zbl0712.65082MR1071622
  11. [11] F. Méhats, Thèse de doctorat de l'École polytechnique, 1997. 
  12. [12] F. Méhats and J.-M. Roquejoffre, A nonlinear oblique derivative boundary value problem for the heat equation. Part 1: Basic results, to appear in Ann. IHP,Analyse Non Linéaire. Zbl0922.35072

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