On a result of K. Masuda concerning reaction-diffusion equations

Global classical solutions for reaction–diffusion systems with nonlinearities of exponential growth

“…The idea for solving the global existence of solutions for the problem (1.1)-(1.4) is a Lyapunov functional. Similar functionals appeared in [6], [3] and [11] . The study of local existence and uniqueness of solution (u, v) of the problem (1.1)-(1.4) follows from the basic existence theory for abstract parabolic semilinear equations (see, e.g., [2], [7], [9] and [15]).…”

“…Our paper mainly complements the investigations of [6], [3], [11] and [16]. We prove the existence of global classical solutions of (1.1)-(1.4) when the reactive terms satisfying (A1)-(A3).…”

“…In [6] A. Haraux and A. Youkana have generalized the method of K. Masuda to handle nonlinearities f (ξ, η) and g(ξ, η) satisfying…”

Boundedness and Large-Time Behavior Results for a Diffusive Epidemic Model

“…When Λ = 0 (which corresponds to the situation where there is no new supply in the susceptible class), a quite similar question was studied by many authors (see [4][5][6]) and a positive answer was first given by Haraux and Youkana [7] using the Lyapunov function techniques (see also [8]) and later on by Kanel (see, e.g., [9]) using useful properties inherent to the underlying Green function.…”

Global solution of reaction diusion system with full matrix

“…Following Masuda's approach, Haraux and Youkana [9] established a global existence result of system (1.1)-(1.3) for a large class of the function f and g. More precisely they showed that for…”