A priori estimate for the second-order derivatives of solutions to the Dirichlet problem for fully nonlinear parabolic equations

1998 ◽  
Vol 92 (6) ◽  
pp. 4302-4315
Author(s):  
N. M. Ivochkina ◽  
S. I. Prokofieva
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Nonlinear Parabolic Equations ◽  
Second Order ◽  
Priori Estimate ◽  
Fully Nonlinear ◽  
Nonlinear Parabolic ◽  
Derivatives Of

Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

2002 ◽  
Vol 9 (3) ◽  
pp. 431-448
Author(s):  
A. Bychowska
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equations ◽  
Unknown Function ◽  
Functional Dependence ◽  
Nonlinear Parabolic Equations ◽  
Quasilinearization Method ◽  
Convergence Theorems ◽  
Nonlinear Parabolic ◽  
Quasilinearization Methods ◽  
Derivatives Of

Abstract We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.

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