scholarly journals A particle method and numerical study of a quasilinear partial differential equation

2011 ◽  
Vol 10 (5) ◽  
pp. 1503-1515 ◽  
Author(s):  
Roberto Camassa ◽  
◽  
Pao-Hsiung Chiu ◽  
Long Lee ◽  
W.-H. Sheu ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Study ◽  
Particle Method ◽  
Partial Differential ◽  
Quasilinear Partial Differential Equation

scholarly journals Convergence of approximate solutions of a quasilinear partial differential equation

1994 ◽  
Vol 50 (3) ◽  
pp. 425-433 ◽  
Author(s):  
T.R. Cranny
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Original Problem ◽  
A Priori ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Special Cases ◽  
Convergence Of Approximate Solutions ◽  
Hölder Estimates ◽  
Quasilinear Partial Differential Equation

This article is a sequel to a paper in which a quasilinear partial differential equation with nonlinear boundary condition was approximated using mollifiers, and the existence of solutions to the approximating problem shown under quite general conditions. In this paper we show that standard a priori Hölder estimates ensure the convergence of these solutions to a classical solution of the original problem. Some partial results giving such estimates for special cases are described.

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