Vanishing, moving and immovable interfaces in fast reaction limits

Spatial-segregation limit for exclusion processes with two components under unbalanced reaction

“…Our aim is to understand this result by conducting the scaling limit of interacting particle systems where the exponents of reaction terms are restricted to be positive integer. For this reason, though [9] also studies CaseIV (moving interface) with its exponent 1 ≤ m 4 < 2 in [9], this can not be derived from our interacting particle system except for the trivial case m 4 = 1 (this case is contained in CaseII).…”

“…We study limiting behavior of interfaces which appear by such a strong competition. Consequently, three kinds of limiting behavior of interfaces (vanishing, moving and immovable interfaces as in [9]) are derived directly from our interacting particle system taking advantage of hydrodynamic limit procedure with singular limit for annihilation dynamics.…”

Fast-reaction limit for Glauber-Kawasaki dynamics with two components

“…The study of the fast-reaction limit in the reaction diffusion systems goes back more than 20 years. The motivation of this study comes from population dynamics [2], [1], [8], massaction kinetics chemistry [3] and others. Consider the system consisted of two types of species, say A and B, and assume each of them moves by diffusion with rates d 1 and d 2 , respectively.…”

Fast reaction limit of reaction-diffusion systems

“…Fast reaction limits of systems with different fast reaction terms in equations for u and v are still far from being well understood. There are some researches on such problems, see, e.g., [4,14]. Quite recently, Iida, Ninomiya and Yamamoto reviewed the recent development of fast reaction limits and reaction-diffusion system approximations [16].…”

“…Assume that (H1)-(H4) are satisfied. Let β and f be the functions defined in (14). Let (u k , v k ) be the weak solutions of (5) with an initial datum (u k 0 , v k 0 ).…”