Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity
Nefedov, N. N. ; Sakamoto, K.
Hiroshima Math. J., Tome 33 (2003) no. 1, p. 391-432 / Harvested from Project Euclid
We deal with reaction-diffusion equations of bistable type in an inhomogeneous medium. When the reaction term is balanced in the sense that a bulk potential energy attains the same global minimum at the two stable equilibria for each spatial point, we derive a free-boundary problem whose solutions determine equilibirum interfaces. We show that a non-degenerate solution of the free-boundary problem gives rise to an equilibrium internal layer solution of the reaction-diffusion equation, and moreover, the stability property of the latter is obtained from a linearization of the free boundary problem.
Publié le : 2003-11-14
Classification:  35K57,  35B25,  35B35
@article{1150997983,
     author = {Nefedov, N. N. and Sakamoto, K.},
     title = {Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity},
     journal = {Hiroshima Math. J.},
     volume = {33},
     number = {1},
     year = {2003},
     pages = { 391-432},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1150997983}
}
Nefedov, N. N.; Sakamoto, K. Multi-dimensional stationary internal layers for spatially inhomogeneous reaction-diffusion equations with balanced nonlinearity. Hiroshima Math. J., Tome 33 (2003) no. 1, pp.  391-432. http://gdmltest.u-ga.fr/item/1150997983/