[Homogénéisation d’une équation de la chaleur semi-linéaire]
Nous considérons l’homogénéisation d’une équation de la chaleur semi-linéaire avec viscosité tendant vers
We consider the homogenization of a semilinear heat equation with vanishing viscosity and with oscillating positive potential depending on
Accepté le :
Publié le :
DOI : 10.5802/jep.54
Keywords: Homogenization, parabolic equations, vanishing viscosity
Mots-clés : Homogénéisation, équations paraboliques, viscosité tendant vers
Annalisa Cesaroni 1 ; Nicolas Dirr 2 ; Matteo Novaga 3

@article{JEP_2017__4__633_0, author = {Annalisa Cesaroni and Nicolas Dirr and Matteo Novaga}, title = {Homogenization of a semilinear heat equation}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {633--660}, publisher = {\'Ecole polytechnique}, volume = {4}, year = {2017}, doi = {10.5802/jep.54}, zbl = {1372.35024}, mrnumber = {3665611}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.54/} }
TY - JOUR AU - Annalisa Cesaroni AU - Nicolas Dirr AU - Matteo Novaga TI - Homogenization of a semilinear heat equation JO - Journal de l’École polytechnique — Mathématiques PY - 2017 SP - 633 EP - 660 VL - 4 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.54/ DO - 10.5802/jep.54 LA - en ID - JEP_2017__4__633_0 ER -
%0 Journal Article %A Annalisa Cesaroni %A Nicolas Dirr %A Matteo Novaga %T Homogenization of a semilinear heat equation %J Journal de l’École polytechnique — Mathématiques %D 2017 %P 633-660 %V 4 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.54/ %R 10.5802/jep.54 %G en %F JEP_2017__4__633_0
Annalisa Cesaroni; Nicolas Dirr; Matteo Novaga. Homogenization of a semilinear heat equation. Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 633-660. doi : 10.5802/jep.54. https://jep.centre-mersenne.org/articles/10.5802/jep.54/
[1] - “Diffusion as a singular homogenization of the Frenkel-Kontorova model”, J. Differential Equations 251 (2011) no. 4-5, p. 785-815 | DOI | MR | Zbl
[2] - Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 1997 | Zbl
[3] - “Some homogenization results for non-coercive Hamilton-Jacobi equations”, Calc. Var. Partial Differential Equations 30 (2007) no. 4, p. 449-466 | DOI | MR | Zbl
[4] - “Counter-example in three dimension and homogenization of geometric motions in two dimension”, Arch. Rational Mech. Anal. 212 (2014) no. 2, p. 503-574 | DOI | MR | Zbl
[5] - “A discussion about the homogenization of moving interfaces”, J. Math. Pures Appl. (9) 91 (2009) no. 4, p. 339-363 | DOI | MR | Zbl
[6] - “Asymptotic speed of propagation for a viscous semilinear parabolic equation”, in Gradient flows: from theory to application, ESAIM Proceedings and Surveys, vol. 54, Société de Mathématiques Appliquées et Industrielles & EDP Sciences, Paris, 2016, p. 45-53 | MR | Zbl
[7] - “Long-time behavior of the mean curvature flow with periodic forcing”, Comm. Partial Differential Equations 38 (2013) no. 5, p. 780-801 | DOI | MR | Zbl
[8] - “Curve shortening flow in heterogeneous media”, Interfaces Free Bound. 13 (2011) no. 4, p. 485-505 | DOI | MR | Zbl
[9] - “Periodic travelling wave solutions of a parabolic equation: a monotonicity result”, J. Math. Anal. Appl. 275 (2002) no. 2, p. 804-820 | DOI | MR | Zbl
[10] - “Pulsating wave for mean curvature flow in inhomogeneous medium”, European J. Appl. Math. 19 (2008) no. 6, p. 661-699 | DOI | MR | Zbl
[11] - “Pinning and de-pinning phenomena in front propagation in heterogeneous media”, Interfaces Free Bound. 8 (2006) no. 1, p. 79-109 | DOI | MR | Zbl
[12] - Surface evolution equations. A level set approach, Monographs in Mathematics, vol. 99, Birkhäuser Verlag, Basel, 2006 | Zbl
[13] - “On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations”, SIAM J. Math. Anal. 42 (2010) no. 5, p. 2155-2176 | DOI | MR | Zbl
[14] - “Homogenization of first-order equations with
[15] - “Singular limits of scalar Ginzburg-Landau equations with multiple-well potentials”, Adv. Differential Equations 2 (1997) no. 1, p. 1-38 | MR | Zbl
[16] - “Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications”, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005) no. 5, p. 667-677 | DOI | Numdam | MR | Zbl
[17] - “Periodic travelling wave solutions of a curvature flow equation in the plane”, Tôhoku Math. J. (2) 59 (2007) no. 3, p. 365-377 | DOI | MR | Zbl
[18] - “Periodic traveling waves of a mean curvature flow in heterogeneous media”, Discrete Contin. Dynam. Systems 25 (2009) no. 1, p. 231-249 | DOI | MR | Zbl
[19] - “Convergence to periodic fronts in a class of semilinear parabolic equations”, NoDEA Nonlinear Differential Equations Appl. 4 (1997) no. 4, p. 521-536 | DOI | MR
[20] - “Homogeneization problems for ordinary differential equations”, Rend. Circ. Mat. Palermo (2) 27 (1978) no. 1, p. 95-112 | DOI | MR | Zbl
[21] - Maximum principles in differential equations, Springer-Verlag, New York, 1984 | DOI | Zbl
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