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Barles and P. Souganidis, A new approach to front propagation problems: Theory and applications ,, Arch. Rational Mech. Bellettini and M. Paolini, Quasi-optimal error estimates for the mean curvature flow with a forcing term ,, Differential Integral Equations , 8 , Berestycki and F.
Bronsard and R. Kohn, Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics ,, J.
Differential Equations , 90 , Chen, Generation and propagation of interfaces for reaction-diffusion equations ,, J. Differential Equations , 96 , Chen, Generation and propagation of interfaces for reaction-diffusion systems ,, Trans. Chen and F. Reitich, Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling ,, J. Chen, Dynamics of interfaces in reaction diffusion systems ,, Hiroshima Math. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations ,, J.
Geometry , 33 , Evans, H. Souganidis, Phase transitions and generalized motion by mean curvature ,, Comm. Pure Appl. Evans and J. Spruck, Motion of level sets by mean curvature. Differential Geometry , 33 , Kawasaki and T. Matano and M. Nara, Large time behavior of disturbed planar fronts in the Allen-Cahn equation ,, J. Edinburgh A , , Schatzman, Geometrical evolution of developed interfaces ,, Trans.
Soner, Ginzburg-Landau equation and motion by mean curvature. Convergence ,, J. Development of the initial interface ,, J.
Thomas I. Interface conditions for a singular reaction-diffusion system.
Stability and asymptotic profile of steady state solutions to a reaction-diffusion pelagic-benthic algae growth model. Continuous dependence in front propagation of convective reaction-diffusion equations. Danielle Hilhorst , Hideki Murakawa. Differential Equations, 19 , Ma, X. Propagation and its failure in a lattice delayed differential equation with global interaction. The global structure of traveling waves in spatially discrete dynamical systems.
Differential Equations, 11 , 49— Entire solutions with merging fronts to reaction-diffusion equations. Differential Equations, 18 , Ninomiya, M. Existence and global stability of traveling curved fronts in the Allen-Cahn equations. Shi, W. Li, C.
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Stability and uniqueness of traveling wavefronts in a two-dimensional lattice differential equation with delay. Smith, H. Strongle order preserving semiflows generated by functional differential equations. Differential Equations, 93 , — Wu, X. Structured population on two patches: Modeling dispersion and delay.
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A reaction-diffusion model for a single species with age structure: I Travelling wavefronts on unbounded domains. Taylor, J. Cahn, C. Geometric models of crystal growth. Acta Metall. Wang, W. Li, S. Travelling wave fronts of reaction-diffusion systems with spatio-temporal delays. Existence and stability of traveling wave fronts in reaction advection diffusion equations. Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity.
Perspectives in Nonliner Partial Differential Equations
Entire solutions in delayed lattice differential equations with monostable nonlinearity. Long-time behavior of a class of biological models. Weng, H. Huang, J. Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction.
The Laplace Transform. Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations. Backward global solutions characterizing annihilation dynamics of travelling fronts. Current usage metrics About article metrics Return to article. Initial download of the metrics may take a while. Table of Contents. Previous article Next article.
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