On nonlinear coupled reaction-diffusion equations
The author proves existence and uniqueness of solutions of coupled reaction-diffusion equations. The interesting fact is that he avoids completely hypothesis of monotone character on the reaction functions in the equations. By means of the Green's function representation he converts the problem into a system of Volterra-Fredholm type integral equations; then he applies Banach fixed point theorems. Finally an application of the obtained results is given for a second order nonlinear evolution equation with strong dissipation.
Volterra-Fredholm type integral equations
scientific article; zbMATH DE number 3957775