Conjugate gradient algorithms in the solution of optimization problems for nonlinear elliptic partial differential equations

Computing ◽  
1979 ◽  
Vol 22 (1) ◽  
pp. 59-77 ◽  
Author(s):  
Dianne P. O'Leary
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Conjugate Gradient Algorithms ◽  
Nonlinear Elliptic ◽  
Gradient Algorithms

On the Dirichlet problem for weakly non-linear elliptic partial differential equations

1977 ◽  
Vol 76 (4) ◽  
pp. 283-300 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Weakly Nonlinear ◽  
Partial Derivatives ◽  
Nonlinear Elliptic ◽  
Non Linear

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.

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