A Fatou Theorem for the General One- Dimensional Parabolic Equation
نویسنده
چکیده
(1.1) du/dt = 9u = a{x)uxx + b{x)ux + c{x)u in R x (0, T) where T ^ oo. Here a(x) ^ 0, c(x) S M, l/«(x), b(x)/a(x) and c(x)/a(x) are locally integrable in R, but otherwise the coefficients are unrestricted. The results below extend characterizations of Widder ([17], [18]) for positive solutions of the heat equation (see §1.1). In particular, we find that all positive solutions of (1.1) are of the form
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