Global existence of solutions for a strongly coupled quasilinear parabolic system

Diffusive and nondiffusive population models

“…Then the diffusion matrix is triangular and the equation (8) for the second species is only weakly coupled through the reaction terms, considerably facilitating the analysis. We mention some works in this direction: Pozio and Tesei [123] have assumed rather restrictive conditions on the reaction terms for their global existence results. The conditions have been weakened later by Yamada [153].…”

Existence result for degenerate cross-diffusion system with application to seawater intrusion

“…The existence of a global solution for such problem in arbitrary space dimension is studied in [31], where the quadratic form of the diffusion matrix is supposed positive definite. On the other hand, the two-species case was frequently studied, see for instance [22,15,30,13,28] for dimensions 1, 2, and [6,25,26,5] for arbitrary dimension and appropriate conditions. Another example of such problems is the electochemistry model studied by Choi, Huan and Lui in [7] where they consider the general form 11) and prove the existence of a weak solution of (1.11) under assumptions on the matrices A l (u) = (a ij l (u)) 1≤i,j≤m : it is continuous in u, its components are uniformly bounded with respect to u and its symmetric part is definite positive.…”

Global existence of solutions for a strongly coupled population system

“…We summarize some of the available results for the timedependent equations (see [13] for a review) and refer to [8] for the stationary problem. Global existence of solutions and their qualitive behavior for α 11 = α 22 = α 21 = 0 have been proved in, e.g., [9,11]. In this case, Eq.…”

“…We assume that α 12 > 0 and α 21 > 0 which is no restriction since if α 12 = 0 or α 21 = 0, at least one of the equations (1), (2) is weakly coupled, and the results of [11] apply. Eqs.…”