WEAK TRAVELING-WAVE FRONT SOLUTIONS OF GENERALIZED DIFFUSION-EQUATIONS WITH REACTION

The author demonstrate that the two-point boundary value problem [GRAPHICS] has a solution (lambdaBAR,pBAR(s)), where Absolute value of lambda is the smallest parameter, under the minimal stringent restrictions on f(s), by applying the shooting and regularization methods. In a classic paper, Kolmogorov et. al. studied in 1937 a problem which can be converted into a special case of the above problem. The author also use the solution (lambdaBAR, pBAR(s)) to construct a weak travelling wave front solution u(x, t) = y(xi),xi = x - Ct, C = lambdaNBAR/(N + 1), of the generalized diffusion equation with reaction [GRAPHICS] where N > 0, k(s) > 0 a.e. on [0, 1], and f(s) := N+1/N integral-s/0 g(t)k1/N (t)dt is absolutely continuous on [0, 1], while y(xi) is increasing and absolutely continuous on (-infinity, +infinity) and (k(y(xi))\y,(xi)\ N)' = g(y(xi)) - Cy'(xi) a.e. on (-infinity,+infinity) and y(-infinity) = 0, y(+infinity) = 1.