Rupture Solutions for a Quasilinear Elliptic Equation Arise from Non-newtonian Filtration
[1]
Zhoujin Cui, Basic Teaching Department, Jiangsu Maritime Institute, Nanjing, China.
[2]
Xiaorong Zhang, Basic Teaching Department, Jiangsu Maritime Institute, Nanjing, China.
The authors considered the rupture solutions for a quasilinear elliptic equation in a finite ball. The purpose of this paper is on the existence of radial point rupture solution. Motivated by the thin film equations, a solution is proved to be a point rupture solution. The main result is a sufficient condition on function for the existence of radial point rupture solutions. The paper conjecture that the ruptures are discrete for finite energy solutions, and expect that the radial point rupture solutions will serve as the blow up profile of the solution near any point rupture.
Quasilinear Elliptic Equation, Thin Film, Point Rupture, Radial Solution, Singular
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