We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space (E, ρ) up to an accuracy of  epsilon > 0 with respect to the L^1-distance. Such an estimate is explicitly computed in terms of…

Geometric dynamical systems ideas have been very successful in determining traveling and standing waves in one space dimension.  Techniques that have proved important for their existence and stability include geometric singular perturbation theory, Lin’s Method, the Evans Function and the Maslov Index. Spatial Dynamics constitutes an approach to extending these ideas to higher-dimensional domains that…

We study a critical case of Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton-Jacobi equation, which results from applying the Bernstein transform to the original Coagulation-Fragmentation equation. Our results include wellposedness, regularity and long-time behaviors of viscosity solutions…