Abstract
AbstractIn this paper we consider the non‐characteristic Cauchy problem ut−a(x)uxx−b(x)ux−c(x)u = 0, x ∈ (0, l), t ∈ I, u(0, t) = φ(t), ux(0, t) = 0, t ∈ I, where I = ℝ or I = ℝ+ and u(x, 0) = 0, x ∈ [0, l], in the case I = ℝ+. Assuming an a priori bound for ‖u(l,.)‖, we derive the exact Hölder type dependence of on ‖u(x,.)‖ on ‖φ‖.
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