scholarly journals Asymptotics for the time-dependent thermistor problem

2004 ◽  
Vol 62 (3) ◽  
pp. 471-476
Author(s):  
Giovanni Cimatti
Keyword(s):  
Time Dependent ◽  
Thermistor Problem

scholarly journals UNIFORM BMO ESTIMATE OF PARABOLIC EQUATIONS AND GLOBAL WELL-POSEDNESS OF THE THERMISTOR PROBLEM

2015 ◽  
Vol 3 ◽  
Author(s):  
BUYANG LI ◽  
CHAOXIA YANG
Keyword(s):  
Parabolic Equations ◽  
Elliptic Equations ◽  
Boundary Data ◽  
Time Dependent ◽  
Well Posedness ◽  
Global Classical Solution ◽  
Thermistor Problem ◽  
Degenerate Elliptic ◽  
Uniqueness Of The Solution ◽  
Temperature Equation

We prove global well-posedness of the time-dependent degenerate thermistor problem by establishing a uniform-in-time bounded mean ocsillation (BMO) estimate of inhomogeneous parabolic equations. Applying this estimate to the temperature equation, we derive a BMO bound of the temperature uniform with respect to time, which implies that the electric conductivity is an $A_{2}$ weight. The Hölder continuity of the electric potential is then proved by applying the De Giorgi–Nash–Moser estimate for degenerate elliptic equations with an $A_{2}$ coefficient. The uniqueness of the solution is proved based on the established regularity of the weak solution. Our results also imply the existence of a global classical solution when the initial and boundary data are smooth.

TIME-DEPENDENT PHENOMENA CAUSED BY THE EC DECAY IN Co2+ [Fe(CN)6]3-

1980 ◽  
Vol 41 (C1) ◽  
pp. C1-239-C1-240 ◽  
Author(s):  
Takayuki Kobayashi ◽  
Tetsuo Kitahara
Keyword(s):  
Time Dependent
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