scholarly journals Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term

2018 ◽  
Vol 114 ◽  
pp. 235-261 ◽  
Author(s):  
Mourad Choulli ◽  
Yavar Kian
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Term ◽  
Zero Order ◽  
Time Dependent ◽  
Order Coefficient ◽  
Dirichlet To Neumann Map ◽  
Logarithmic Stability

Computational determination of the lowest order coefficient in a parabolic equation

2014 ◽  
Vol 89 (2) ◽  
pp. 179-181 ◽  
Author(s):  
P. N. Vabishchevich ◽  
V. I. Vasil’ev
Keyword(s):  
Parabolic Equation ◽  
Order Coefficient

scholarly journals Determination of a diffusion coefficient in a quasilinear parabolic equation

2017 ◽  
Vol 15 (1) ◽  
pp. 77-91 ◽  
Author(s):  
Fatma Kanca
Keyword(s):  
Diffusion Coefficient ◽  
Parabolic Equation ◽  
Numerical Experiments ◽  
Input Data ◽  
Quasilinear Parabolic Equation ◽  
Nonlocal Boundary ◽  
Time Dependent ◽  
Integral Overdetermination ◽  
Quasilinear Parabolic

Abstract This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown. Finally, some numerical experiments are presented.

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