PERIODIC AND POSITIVE WAVE-FRONT SOLUTIONS OF SEMILINEAR DIFFUSION-EQUATIONS

The objective of this work is to study the existence of positive and T -periodic undulatory solutions of the form u(x, t) = u(x - c(t)) to th e equation partial derivative u/partial derivative t = Delta u + b(t) del u + f(u), x epsilon Omega, where b = b(t) is T-periodic and the re action term f = f(u) is supposed to satisfy f(u) less than or equal to 0 for 0 < u(0) less than or equal to u. The waves are analyzed in bou nded domains Omega wherein they are subject to special homogeneous Dir ichlet conditions. The average mu of b(t) over the interval (0, T) and the size of Omega are observed as bifurcation parameters. The one-dim ensional version of this Dirichlet problem is deeply and geometrically studied by means of chains of travelling waves to the equation u(t) = u(xx) + f(u), which connect (infinitely many in some cases) zeros of f(u).