Existence results for a fourth order partial differential equation arising in condensed matter physics
Carlos Escudero; Filippo Gazzola; Robert Hakl; Ireneo Peral; Pedro José Torres
Mathematica Bohemica (2015)
- Volume: 140, Issue: 4, page 385-393
- ISSN: 0862-7959
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topEscudero, Carlos, et al. "Existence results for a fourth order partial differential equation arising in condensed matter physics." Mathematica Bohemica 140.4 (2015): 385-393. <http://eudml.org/doc/271802>.
@article{Escudero2015,
abstract = {We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions.},
author = {Escudero, Carlos, Gazzola, Filippo, Hakl, Robert, Peral, Ireneo, Torres, Pedro José},
journal = {Mathematica Bohemica},
keywords = {higher order parabolic equation; existence of solution; blow-up in finite time; higher order elliptic equation; variational method; strongly singular boundary value problem},
language = {eng},
number = {4},
pages = {385-393},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence results for a fourth order partial differential equation arising in condensed matter physics},
url = {http://eudml.org/doc/271802},
volume = {140},
year = {2015},
}
TY - JOUR
AU - Escudero, Carlos
AU - Gazzola, Filippo
AU - Hakl, Robert
AU - Peral, Ireneo
AU - Torres, Pedro José
TI - Existence results for a fourth order partial differential equation arising in condensed matter physics
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 385
EP - 393
AB - We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions.
LA - eng
KW - higher order parabolic equation; existence of solution; blow-up in finite time; higher order elliptic equation; variational method; strongly singular boundary value problem
UR - http://eudml.org/doc/271802
ER -
References
top- Escudero, C., Gazzola, F., Peral, I., Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian, J. Math. Pures Appl. (9) 103 (2015), 924-957. (2015) MR3318175
- Escudero, C., Hakl, R., Peral, I., Torres, P. J., 10.1002/mma.2836, Math. Methods Appl. Sci. 37 (2014), 793-807. (2014) MR3188526DOI10.1002/mma.2836
- Escudero, C., Hakl, R., Peral, I., Torres, P. J., 10.1017/S0956792512000484, Eur. J. Appl. Math. 24 (2013), 437-453. (2013) Zbl1266.91051MR3053654DOI10.1017/S0956792512000484
- Escudero, C., Peral, I., 10.1016/j.jde.2012.12.012, J. Differ. Equations 254 (2013), 2515-2531. (2013) Zbl1284.35435MR3016212DOI10.1016/j.jde.2012.12.012
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