A two-grid algorithm based on expanded mixed element discretizations for strongly nonlinear elliptic equations

2014 ◽  
Vol 70 (1) ◽  
pp. 93-111 ◽  
Author(s):  
Wei Liu ◽  
Zhe Yin ◽  
Jin Li
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Grid Algorithm ◽  
Mixed Element ◽  
Element Discretizations

Existence results for diffusion–convection equations of nonlinear unilateral problems defined in Orlicz–Sobolev spaces

2018 ◽  
Vol 11 (06) ◽  
pp. 1850079
Author(s):  
H. Moussa ◽  
M. Rhoudaf ◽  
H. Sabiki
Keyword(s):  
Elliptic Equations ◽  
Order Term ◽  
Nonlinear Elliptic Equations ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Polynomial Type ◽  
Carathéodory Function ◽  
Unilateral Problems ◽  
The Right ◽  
Diffusion Convection

We prove the existence result of unilateral problems associated to strongly nonlinear elliptic equations whose model, including the diffusion–convection equation, is [Formula: see text]. We study exactly the following general case [Formula: see text] where [Formula: see text] is a Leray–Lions operator having a growth not necessarily of polynomial type, the lower order term [Formula: see text] : [Formula: see text] is a Carathéodory function, for a.e. [Formula: see text] and for all [Formula: see text] satisfying only a growth condition and the right-hand side [Formula: see text] belongs to [Formula: see text].

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