Existence for a Class of p-Laplace Evolution Equation
Haixin Zhang · Journal of Nantong University · 2013
This paper studies the existence and uniqueness of solutions for a class of p-Laplace evolution equation u t= div(Δu p- 2 Δu) + aurΩ乙uq(x, t)dx in a bounded domain Ω奂RN with N 2, where Δp u = div(Δu p- 2 Δu)with p 1, and r, q 0. It is shown that the local solution exists and if r, q ≥ 1, the solution is unique and if r, q 1, the uniqueness doesn't always hold.