Almost periodic homogenization of Hamilton-Jacobi equations

By Hitoshi Ishii. 2000

82 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c9f2361c93a0c7d367abbc3ed7fb59f866ae6640

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Ergodic Type Problems and Large Time Behaviour of Unbounded Solutions of Hamilton–Jacobi Equations (2006, background): “They also arise in homogenization theory (the so-called cell problems) and a related question to ours is whether the periodicity assumption on H can be removed while keeping bounded solutions (the correctors): We refer to Ishii (2000) for the existence of bounded approximate correctors in the almost”
Some homogenization results for non-coercive Hamilton–Jacobi equations (2006, background): “Ishii[24]) and for Hamiltonians with stochastic dependence (cf.”
Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media (2005, methodology): “It is, however, a straightforward modification of Ishii [13] that treats almost periodic Hamilton-Jacobi equations.”
Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations (2012, methodology): “[8] I. Capuzzo-Dolcetta and H. Ishii.”
Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media (2010, background): “It is then follows (see [22 ]a nd [ 14 ] for such arguments) that, as e → 0, ue →¯ u where ¯ u is the solution of (1.2) with ¯”
Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications (2005, unknown): “Ishii in [20] considered the homogenization of Hamilton–Jacobi equa almost periodic settings.”
Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case (2009, background): “For instance in [16] Lions and Souganidis tackle this issues and exploit a Crandall’s result on Eikonal Hamiltonians to construct a 1–dimensional example showing that bounded approximate correctors in general do not exist, in contrast to what happens in the almost periodic case, see [2, 13] The poin”