关键词: 抛物方程, 权函数, L^∞估计

Abstract: The author considered a parabolic partial differential equation with weight function. By using Giorgi’s iteration technique, the maximal norm estimate of weak solution sequence of the perturbation problem of the equation was given. By means of the energy estimate and Simon’s compactness theorem, the existence of weak solutions of the equation was proved by the limit process.

Key words: parabolic equation, weight function, L^∞ estimate