Global existence in reaction–diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects

Global existence and fast-reaction limit in reaction-diffusion systems with cross effects

Tracking based motion segmentation under relaxed statistical assumptions

Many Computer Vision algorithms employ the sum of pixel-wise squared differences between two patches as a statistical measure of similarity. This silently assumes that the noise in every pixel is independent. We present a method that involves a much more general noise model with relaxed independence assumptions but without significant increase in the computational requirements. We apply this te...

Existence Assumptions in Knowledge Representation

Hirst, G., Existence assumptions in knowledge representation, Artificial Intelligence 49 (1991) 199-242. If knowledge representation formalisms are to be suitable for semantic interpretation of natural language, they must be more adept with representations of existence and nonexistence than they presently are. Quantifiers must sometimes scope over nonexistent entities. I review the philosophica...

On Global Existence of Solutions to a Cross-diffusion System

the Laplacian, ∂/∂ν denotes the directional derivative along the outward normal on ∂Ω, ai, bi, ci, di (i = 1, 2) are given positive constants and α, γ, δ, β are nonnegative constants. In the system (1.1) u and v are non-negative functions which represent population densities of two competing species, d1 and d2 are respectively their diffusion rates. Parameters a1 and a2 are intrinsic growth rat...

Global Well-Posedness of a Conservative Relaxed Cross Diffusion System

We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form ui → ∂tui − ∆(ai(ũ)ui) where the ui, i = 1, ..., I represent I density-functions, ũ is a spatially regularized form of (u1, ..., uI) and the nonlinearities ai are merely assumed to be continuous and bounded from below. Existence of global weak solutions is o...