Uniqueness Of Weak Solutions Of The Cauchy Problem For Doubly Nonlinear Parabolic Equations

The Cauchy problem for the non-newton polypropic filtration equationis considered in this paper, where m≥1,p≥ 2. After giving the definition of the weak solution of the equation above, and assuming that 0 ≤ u₀(x) ∈ L¹(Rⁿ) ∩L^∞(Rⁿ), a new result about the uniqueness of weak solutions of this equation is obtained. The main tools used in the proofs are Steklov mean value method, partial summation skill and Kruzhkov's method of doubling variables both in space and time. A comparison principle is obtained and the uniqueness of weak solutions of the Cauchy problem is proved.