Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability

We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under

The problem is split in two parts: A hyperbolic term solved by using the Hopf and Lax formula and a parabolic term solved by a backward linearized Euler method in time and a

We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations

The existence of the family of solutions does not allow one to use directly the topological degree because there is a zero eigenvalue of the linearized problem and a uniform a

Keywords: traveling wave, spectral stability, orbital stability, Hamiltonian dynamics, action, mass Lagrangian coordinates.. AMS Subject Classifications: 35B10; 35B35; 35Q35;

We establish a convergence theorem for a class of nonlinear reaction-diffusion equations when the diffusion term is the subdifferential of a convex functional in a class of

We see that the growth of amplitude modulation causes de- creasing of instability increment to the value which makes possible the existence of wave chains observed in /I/..

Finally, this theorem shows that the family of spherically symmetric travel- ling waves is not asymptotically stable for arbitrary perturbations: this means that the higher