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A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji 192-0397, Japan |
Chen, Kung and Morita [
Motivated by [
References:
[1] |
H. Brezis,
Functional Analysis, Sobolev Spaces and Partial Differencial Equations Springer, New York, 2010. |
[2] |
D. Bonheure and L. Sanchez,
Heteroclinic orbits for some classes of second and fourth order differential equations, Handbook of Differential Equations, 3 (2006), 103-202.
doi: 10.1016/S1874-5725(06)80006-4. |
[3] |
C. N. Chen and Y. Choi,
Standing pulse solutions to FitzHugh-Nagumo equations, Arch. Ration. Mech. Anal., 206 (2012), 741-777.
doi: 10.1007/s00205-012-0542-3. |
[4] |
C. N. Chen, P. van Heijster, Y. Nishiura and T. Teramoto, Localized patterns in a three-component FizHugh-Nagumo model revisited via an action functional J. Dyn. Diff. Equat. (2016), doi:10.1007/s10884-016-9557-z. |
[5] |
C. N. Chen, S. Y. Kung and Y. Morita,
Planar Standing wavefronts in the FitzHugh-Nagumo equations, SIAM J. Math. Anal., 46 (2014), 657-690.
doi: 10.1137/130907793. |
[6] |
E. N. Dancer and S. Yan,
A minimization problem associated with elliptic systems of FitzHugh-Nagumo type, Ann. Inst. H. Poincaré Anal. Non Linéaire, 21 (2004), 237-253.
doi: 10.1016/S0294-1449(03)00032-5. |
[7] |
S. Ei and H. Ikeda,
Front dynamics in heterogeneous diffusive media, Physica D, 239 (2010), 1637-1649.
doi: 10.1016/j.physd.2010.04.008. |
[8] |
T. Kajiwara and K. Kurata, On a variational problem arising from the three-component FitzHugh-Nagumo type reaction-diffusion systems,
Tokyo J. Math. accepted, 2016. |
[9] |
Y. Nishiura, T. Teramoto and X. Yuan,
Heterogeneity-introduced spot dynamics for a three-component reaction-diffusion system, Comm. Pure Appl. Anal., 11 (2012), 307-338.
doi: 10.3934/cpaa.2012.11.307. |
[10] |
Y. Oshita,
On stable nonconstant stationary solutions and mesoscopic patterns for FitzHugh-Nagumo equations in higher dimensions, J. Differential Equations, 188 (2003), 110-134.
doi: 10.1016/S0022-0396(02)00084-0. |
[11] |
C. Sourdis,
The heteroclinic connection problem for general double-well potentials, Mediterr. J. Math., 13 (2016), 4693-4710.
doi: 10.1007/s00009-016-0770-0. |
show all references
References:
[1] |
H. Brezis,
Functional Analysis, Sobolev Spaces and Partial Differencial Equations Springer, New York, 2010. |
[2] |
D. Bonheure and L. Sanchez,
Heteroclinic orbits for some classes of second and fourth order differential equations, Handbook of Differential Equations, 3 (2006), 103-202.
doi: 10.1016/S1874-5725(06)80006-4. |
[3] |
C. N. Chen and Y. Choi,
Standing pulse solutions to FitzHugh-Nagumo equations, Arch. Ration. Mech. Anal., 206 (2012), 741-777.
doi: 10.1007/s00205-012-0542-3. |
[4] |
C. N. Chen, P. van Heijster, Y. Nishiura and T. Teramoto, Localized patterns in a three-component FizHugh-Nagumo model revisited via an action functional J. Dyn. Diff. Equat. (2016), doi:10.1007/s10884-016-9557-z. |
[5] |
C. N. Chen, S. Y. Kung and Y. Morita,
Planar Standing wavefronts in the FitzHugh-Nagumo equations, SIAM J. Math. Anal., 46 (2014), 657-690.
doi: 10.1137/130907793. |
[6] |
E. N. Dancer and S. Yan,
A minimization problem associated with elliptic systems of FitzHugh-Nagumo type, Ann. Inst. H. Poincaré Anal. Non Linéaire, 21 (2004), 237-253.
doi: 10.1016/S0294-1449(03)00032-5. |
[7] |
S. Ei and H. Ikeda,
Front dynamics in heterogeneous diffusive media, Physica D, 239 (2010), 1637-1649.
doi: 10.1016/j.physd.2010.04.008. |
[8] |
T. Kajiwara and K. Kurata, On a variational problem arising from the three-component FitzHugh-Nagumo type reaction-diffusion systems,
Tokyo J. Math. accepted, 2016. |
[9] |
Y. Nishiura, T. Teramoto and X. Yuan,
Heterogeneity-introduced spot dynamics for a three-component reaction-diffusion system, Comm. Pure Appl. Anal., 11 (2012), 307-338.
doi: 10.3934/cpaa.2012.11.307. |
[10] |
Y. Oshita,
On stable nonconstant stationary solutions and mesoscopic patterns for FitzHugh-Nagumo equations in higher dimensions, J. Differential Equations, 188 (2003), 110-134.
doi: 10.1016/S0022-0396(02)00084-0. |
[11] |
C. Sourdis,
The heteroclinic connection problem for general double-well potentials, Mediterr. J. Math., 13 (2016), 4693-4710.
doi: 10.1007/s00009-016-0770-0. |
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