Nonlinear Reaction-Diffusion Systems

Publisher Summary This chapter discusses nonlinear reaction–diffusion systems. An example is illustrated in the chapter of a system where both of the diffusion coefficients are positive and a solution blows up in finite time even though the associated ordinary equation has the global existence property for all nonnegative initial data. The chapter also considers a simple 2 x 2 system of partial differential equations (P.D.E) for which the associated ordinary differential equations (O.D.E.) has the global existence and positivity properties but where usual arguments like maximum principle or invariant regions techniques do not apply. The basic method for polynomial growth is also presented in the chapter for a 2 x 2 system with general and different diffusions. In the chapter, “critical” boundary conditions and L1-technique is also discussed.