scholarly journals Stability estimate for a strongly coupled parabolic system

2012 ◽  
Vol 43 (1) ◽  
Author(s):  
Kun-Chu Chen
Keyword(s):  
Parabolic System ◽  
Stability Estimate ◽  
Strongly Coupled

scholarly journals Stability estimate for a strongly coupled parabolic system

2012 ◽  
Vol 43 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Kun-Chu Chen
Keyword(s):  
Parabolic System ◽  
Stability Estimate ◽  
Carleman Estimates ◽  
Inverse Source Problem ◽  
Lipschitz Stability ◽  
Strongly Coupled

We consider an inverse source problem for a 2×2 strongly coupled parabolic system. The Lipschitz stability is proved and the proof is based on the Carleman estimates with two large parameters.

Inverse problem for a degenerate/singular parabolic system with Neumann boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed Alaoui ◽  
Abdelkarim Hajjaj ◽  
Lahcen Maniar ◽  
Jawad Salhi
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Source Term ◽  
Neumann Boundary ◽  
Stability Estimate ◽  
Carleman Estimates ◽  
Well Posedness ◽  
Degenerate Diffusion ◽  
Neumann Type ◽  
Lower Order Terms

AbstractIn this paper, we study an inverse source problem for a degenerate and singular parabolic system where the boundary conditions are of Neumann type. We consider a problem with degenerate diffusion coefficients and singular lower-order terms, both vanishing at an interior point of the space domain. In particular, we address the question of well-posedness of the problem, and then we prove a stability estimate of Lipschitz type in determining the source term by data of only one component. Our method is based on Carleman estimates, cut-off procedures and a reflection technique.

scholarly journals Global and nonglobal existence for a strongly coupled parabolic system on a general domain

2016 ◽  
Vol 261 (6) ◽  
pp. 3344-3365 ◽  
Author(s):  
Ricardo Castillo ◽  
Miguel Loayza ◽  
Crislene S. Paixão
Keyword(s):  
Parabolic System ◽  
Strongly Coupled ◽  
General Domain

Heat and sweat transport in fibrous media with radiation

2014 ◽  
Vol 25 (3) ◽  
pp. 307-327 ◽  
Author(s):  
JILU WANG ◽  
WEIWEI SUN
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Parabolic System ◽  
Radiative Heat ◽  
Radiation Transport ◽  
Fibrous Media ◽  
Strongly Coupled ◽  
System A ◽  
Nonlinear Parabolic ◽  
Non Local

The paper is concerned with heat and sweat transport in porous textile media with a non-local thermal radiation and phase change. The model, based on a combination of these classical heat transfer mechanisms (convection, conduction and radiation), is governed by a nonlinear, degenerate and strongly coupled parabolic system. The thermal radiative flow is described by a radiation transport equation and characterized by the thermal absorptivity and emissivity of fibre. A conservative boundary condition is introduced to describe the radiative heat flux interacting with environment. With the conservative boundary condition, we prove the global existence of positive/non-negative weak solutions of a nonlinear parabolic system. A typical clothing assembly with a polyester batting material sandwiched in two laminated covers is investigated numerically. Numerical results show that the contribution of radiative heat transfer is comparable with that of conduction/convection in the sweating system.

scholarly journals Non-negative global weak solutions for a degenerate parabolic system modelling thin films driven by capillarity

2012 ◽  
Vol 142 (5) ◽  
pp. 1071-1085 ◽  
Author(s):  
Bogdan-Vasile Matioc
Keyword(s):  
Parabolic System ◽  
Weak Solutions ◽  
Driving Mechanism ◽  
System Modelling ◽  
Global Weak Solutions ◽  
Degenerate Parabolic System ◽  
Strongly Coupled ◽  
Fluid Layers ◽  
Order Degenerate ◽  
Degenerate Parabolic

We prove the global existence of non-negative weak solutions for a strongly coupled, fourth-order degenerate parabolic system governing the motion of two thin fluid layers in a porous medium when capillarity is the sole driving mechanism.

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