TRAVELING FRONTS IN CYLINDERS

This work is concerned with travelling front solutions of semilinear parabolic equations in an infinite cylindrical domain SIGMA = R x omega where omega subset-of R(n-1) is a bounded domain. We write for x in SIGMA, x = (x1, y), with gamma is-an-element-of omega. The problems we consider are of the following type [GRAPHICS] where the unknowns are the parameter c is-an-element-of R and the function u. The function alpha is-an-element-of C0 (omegaBAR) and the nonlinear term f:[0, 1] --> R are given. (More general coefficients than c + alpha (y), beta (y, c) are also treated.) We obtain a fairly general resolution of this problem. The results depend on the type of nonlinearity considered. When f is of the. bistable type, or of the "ignition temperature" type in combustion, we show the existence and uniqueness of c and of the profile u. In the case that f > 0 in (0, 1), we show the existence of c* is-an-element-of R such that a solution exists if and only if c greater-than-or-equal-to c*. These results extend to higher dimensions various classical results. In particular they extend the result of Kolmogorov, Petrovsky and Piskounov.