scholarly journals Kobayashi–Warren–Carter type systems with nonhomogeneous Dirichlet boundary data for crystalline orientation

2022 ◽  
Vol 217 ◽  
pp. 112722
Author(s):  
Salvador Moll ◽  
Ken Shirakawa ◽  
Hiroshi Watanabe
Keyword(s):  
Boundary Data ◽  
Dirichlet Boundary ◽  
Type Systems ◽  
Crystalline Orientation ◽  
Dirichlet Boundary Data

scholarly journals Solutions toH-systems by topological and iterative methods

2003 ◽  
Vol 2003 (9) ◽  
pp. 539-545 ◽  
Author(s):  
P. Amster ◽  
M. C. Mariani
Keyword(s):  
Iterative Methods ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Newton Iteration ◽  
Dirichlet Boundary Data

We studyH-systems with a Dirichlet boundary datag. Under some conditions, we show that if the problem admits a solution for some(H0,g0), then it can be solved for any(H,g)close enough to(H0,g0). Moreover, we construct a solution of the problem applying a Newton iteration.

scholarly journals Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

2017 ◽  
Vol 17 (4) ◽  
pp. 739-767 ◽  
Author(s):  
Luan T. Hoang ◽  
Thinh T. Kieu
Keyword(s):  
Porous Media ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Time Derivative ◽  
Compressible Fluids ◽  
Time Dependent ◽  
Asymptotic Estimates ◽  
Slightly Compressible ◽  
Interior Estimates ◽  
Dirichlet Boundary Data

AbstractThe generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time, the interior {L^{\infty}}-estimates for the pressure, its gradient and time derivative, and the interior {L^{2}}-estimates for its Hessian. The De Giorgi and Ladyzhenskaya–Uraltseva iteration techniques are used taking into account the special structures of the equations for both pressure and its gradient. These are combined with the uniform Gronwall-type bounds in establishing the asymptotic estimates when time tends to infinity.

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