Math @ Duke

Publications [#287357] of James H. Nolen
Papers Published
 Cardaliaguet, P; Nolen, J; Souganidis, PE, Homogenization and Enhancement for the GEquation,
Archive for Rational Mechanics and Analysis, vol. 199 no. 2
(2011),
pp. 527561, Springer Nature, ISSN 00039527 [4160], [doi]
(last updated on 2023/03/21)
Abstract: We consider the socalled Gequation, a level set HamiltonJacobi equation used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatiotemporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic firstorder (spatiotemporal homogeneous) level set equation. Moreover, we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally, we also consider advection depending on position at the integral scale. © 2010 SpringerVerlag.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

