Front propagation for reaction-diffusion equations of bistable type

G. Barles; L. Bronsard; P. E. Souganidis

Annales de l'I.H.P. Analyse non linéaire (1992)

  • Volume: 9, Issue: 5, page 479-496
  • ISSN: 0294-1449

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Barles, G., Bronsard, L., and Souganidis, P. E.. "Front propagation for reaction-diffusion equations of bistable type." Annales de l'I.H.P. Analyse non linéaire 9.5 (1992): 479-496. <http://eudml.org/doc/78289>.

@article{Barles1992,
author = {Barles, G., Bronsard, L., Souganidis, P. E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular perturbation; reaction diffusion equation; bistable nonlinear term; interface; viscosity solutions},
language = {eng},
number = {5},
pages = {479-496},
publisher = {Gauthier-Villars},
title = {Front propagation for reaction-diffusion equations of bistable type},
url = {http://eudml.org/doc/78289},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Barles, G.
AU - Bronsard, L.
AU - Souganidis, P. E.
TI - Front propagation for reaction-diffusion equations of bistable type
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 5
SP - 479
EP - 496
LA - eng
KW - singular perturbation; reaction diffusion equation; bistable nonlinear term; interface; viscosity solutions
UR - http://eudml.org/doc/78289
ER -

References

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  1. [AC] S. Allen and J. Cahn, A Microscopic Theory for Antiphase Boundary Motion and its Application to Antiphase Domain Coarsening, Acta Metall., Vol. 27, 1979, pp. 1084-1095. 
  2. [AW] D.G. Aronson and H. Weinberger, Multidimensional Nonlinear Diffusion Arising in Population Genetics, Adv. Math., Vol. 30, 1978, pp. 33-76. Zbl0407.92014MR511740
  3. [B] G. Barles, A Remark on a Flame Propagation Model, Rapport I.N.R.I.A., #464, 1985. 
  4. [BES] G. Barles, L.C. Evans and P.E. Souganidis, Wavefront Propagation for Reaction-Diffusion Systems of PDE, Duke U. Math. J., Vol. 61, 1990. Zbl0749.35015MR1084462
  5. [BP] G. Barles and B. Perthame, Exit Time Problems in Optimal Control and the Vanishing Viscosity Method, S.I.A.M. J. Cont. Opt., Vol. 26, 1988, pp. 113-148. Zbl0674.49027MR957658
  6. [BS] G. Barles and P.E. Souganidis, Convergence of Approximation Schemes for Fully Nonlinear Second Order Equations, J. Asympt. Analysis, 1991, pp. 271-283. Zbl0729.65077MR1115933
  7. [BSS] G. Barles, M.H. Soner and P.E. Souganidis, in preparation. 
  8. [BK1] L. Bronsard and R.V. Kohn, Motion by Mean Curvature as the Singular Limit of Ginzburg-London Dynamics, J. Diff. Eq. (to appear). Zbl0735.35072
  9. [BK2] L. Bronsard and R.V. Kohn, On the Slowness of Phase Boundary Motion in One Space Dimension, Comm. Pure Appl. Math. (to appear). Zbl0761.35044MR1075075
  10. [Ca] G. Caginalp, A Conserved Phase Field System; Implication for Kinetic Undercooling, Phys. Rev. B.(to appear). 
  11. [CaF] G. Caginalp and P. Fife, Dynamics of Layered Interfaces Arising from Phase Boundaries, S.I.A.M. J. Applied Math., Vol. 48, 1988, pp. 506-518. MR941098
  12. [Ch] X. Chen, Generation and Propagation of the Interface for Reaction-Diffusion Equations, J. Diff. Eq. (to appear). Zbl0765.35024MR1153311
  13. [CP] J. Carr and R. Pego, Patterns in Solutions of ut = ∈2uxx-f(u), Comm. Pure Appl. Math., Vol. 42, 1989, pp. 523-576. Zbl0685.35054MR997567
  14. [CrIL] M.G. Crandall, H. Ishii and P.-L. Lions, Uniqueness of Viscosity Solutions Revisited, J. Math. Soc. Japan, Vol. 39, 1987, pp. 581-596. Zbl0644.35016MR905626
  15. [CrL] M.G. Crandall and P.-L. Lions, Viscosity Solutions of Hamilton-Jacobi Equations, Trans. A.M.S., Vol. 277, 1983, pp. 1-42. Zbl0599.35024MR690039
  16. [DS1] P. DeMottoni and M. Schatzman, Geometrical Evolution of Developed Interfaces (preprint). 
  17. [DS2] P. DeMottoni and M. Schatzman, Development of Interfaces in RN (preprint). 
  18. [EI] L.C. Evans and H. Ishii, A PDE Approach to Some Asymptotic Problems Concerning Random Differential Equations with Small Noise Intensities, Ann. Inst. H. Poincaré, A.N.L., Vol. 2, 1985, pp. 1-20. Zbl0601.60076MR781589
  19. [ES1] L.C. Evans and P.E. Souganidis, A PDE Approach to Geometric Optics for Certain Reaction-Diffusion Equations, Ind. Un. Math. J., Vol. 38, 1989, pp. 141- 172. Zbl0692.35014MR982575
  20. [ES2] L.C. Evans and P.E. Souganidis, A PDE Approach to Certain Large Deviation Problems for Systems of Parabolic Equations, A.N.L., Contributions en l'honneur de J.-J. Moreau, Gauthier-Villars, 1989. Zbl0679.60040MR1019116
  21. [ESS] L.C. Evans, H.M. Soner and P.E. Souganidis, The Allen-Cahn Equation and Generalized Motion by Mean Curvature (in preparation). 
  22. [FH] P.C. Fife and L. Hsiao, The Generation and Propagation of Internal Layers, J. Non-Linear Anal. (to appear). Zbl0685.35055
  23. [FH] G. Fusco and J. Hale, Slow Motion Manifold, Dormant Instability and Singular Perturbation, J. Dyn. and Diff. Eqs., Vol. 1, 1989, pp. 75-94. Zbl0684.34055MR1010961
  24. [Fi] P. Fife, Dynamics of Internal Layers and Diffusive Interfaces, C.B.M.S.-N.S.F., Regional Conference Series in Applied Math., No. 53, S.I.A.M., Philadelphia. Zbl0684.35001MR981594
  25. [F1] W.H. Fleming, Stochastic Control for Small Noise Intensities, S.I.A.M. J. Control., Vol. 9, 1971, pp. 473-517. Zbl0218.93024MR304045
  26. [FlS] W.H. Fleming and P.E. Souganidis, PDE-Viscosity Solution Approach to Some Problems of Large Deviations, An. Scuola Norm. Sup., Vol. 13, 1986, pp. 171-192. Zbl0622.60032MR876121
  27. [Fr1] M.I. Freidlin, Limit Theorems for Large Deviations and Reaction-Diffusion Equations, Annals of Prob., Vol. 13, 1985, pp. 639-675. Zbl0576.60070MR799415
  28. [Fr2] M.I. Freidlin, Functional Integration and Partial Differential Equations, Annals of Math. Studies109, Princeton University Press, Princeton, 1985. Zbl0568.60057MR833742
  29. [G] J. Gärtner, Bistable Reaction-Diffusion Equations and Excitable Media, Math. Nachr., Vol. 112, 1983, pp. 125-152. Zbl0548.35069MR726855
  30. [GSS] J. Gunton, M. San Miguel and P. Sahni, The Dynamics of First-Order Phase Transitions, in Phase Transitions and Critical Phenomena, C. DOMB and J. LIEBOWITZ Eds., Vol. 8, 1983, pp. 267-466. MR794319
  31. [I] H. Ishii, Hamilton-Jacobi Equations with Discontinuous Hamiltonians on Arbitrary Open Sets, Bull. Fac. Sci. Eng. Chuo Univ., Vol. 28, 1985, pp. 33-77. Zbl0937.35505MR845397
  32. [L] P.-L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. Zbl0497.35001MR667669
  33. [LSV] P.-L. Lions, P.E. Souganidis and J.L. Vazquez, The Relation Between the Porous-Medium and Eikonal Equations in Several Space Dimensions, Rev. Mat. Iberoamericana, Vol. 3, 1987, pp.275-310. Zbl0697.35012MR996819
  34. [P] R. Rpego,Front Migration in the Nonlinear Cahn-Hilliard Equation, Proc. R. Soc. Lond., Vol. A422, 1989, pp. 261-278. Zbl0701.35159MR997638
  35. [RSK] J. Rubinstein, P. Sternberg and J.B. Keller, Fast Reaction, Slow Diffusion, and Curve Shortening, S.I.A.M. Appl. Math., Vol. 49, 1989, pp. 116-133. Zbl0701.35012MR978829

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