scholarly journals Existence result for a doubly degenerate quasilinear stochastic parabolic equation

2005 ◽  
Vol 81 (5) ◽  
pp. 89-94 ◽  
Author(s):  
Mamadou Sango
Keyword(s):  
Parabolic Equation ◽  
Existence Result ◽  
Stochastic Parabolic Equation

scholarly journals Rescaling nonlinear noise for 1D stochastic parabolic equations

2019 ◽  
Vol 20 (04) ◽  
pp. 2050027
Author(s):  
Beniamin Goldys ◽  
Misha Neklyudov
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Space Variable ◽  
Nonlinear Noise ◽  
Stochastic Parabolic Equation

We show regularization effect of nonlinear gradient noise to the solution of 1D stochastic parabolic equation. We demonstrate convergence to a martingale (independent upon space variable) when we rescale noise at the extremum points of the process.

scholarly journals Semi-classical solutions for a nonlinear coupled elliptic-parabolic problem

2007 ◽  
Vol 76 (3) ◽  
pp. 369-396 ◽  
Author(s):  
Catherine Choquet
Keyword(s):  
Porous Media ◽  
Parabolic Equation ◽  
Nonlinear System ◽  
Weak Solutions ◽  
Parabolic Problem ◽  
Existence Result ◽  
Classical Solutions ◽  
Fully Nonlinear ◽  
Strongly Coupled ◽  
Degenerate Form

We give an existence result for a fully nonlinear system consisting of a parabolic equation strongly coupled with an elliptic one. It models in particular miscible displacement in porous media. To this aim, we adapt the tools of Ladyzenskaja, Solon-nikov and Uralćeva [27, 28] to the coupled nonlinear setting. Under some reasonable assumptions on the data, we state the existence of semi-classical solutions for the problem. We also give an existence result of weak solutions for a degenerate form of the problem.

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