zbMATH — the first resource for mathematics

A new approach to front propagation problems: theory and applications. (English) Zbl 0904.35034
The authors give a definition for front propagation with normal velocity which is inspired by the notion of barriers introduced by De Giorgi. They show that this definition is equivalent to the level-set formulation for the evolution. Then they study the asymptotics of the flow under consideration. Having presented some general results they consider examples, namely reaction-diffusion equations with double-well potential, two types of semilinear reaction-diffusion equations, reaction-diffusion equations with oscillatory coefficients, two types of nonlocal fully nonlinear equations, and stochastic Ising models. The paper has a great overlap with the article “Front Propagation: Theory and Applications” by P. E. Souganidis [Lect. Notes Math. 1660, 186-242 (1997; Zbl 0882.35016)].

35K57 Reaction-diffusion equations
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
45K05 Integro-partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI