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IPM Positions 

Non Resident Researcher (nonresident), School of Mathematics
(2001  2002 ) 

Past IPM Positions 

Associate Researcher (nonresident), School of Mathematics
(2000  2001) 

Research Activities 

In the previous works, we applied shapemeasure method to find the optimal
domain (in plan) for control systems governed by elliptic and wave equations
with the given conditions. Here we intend to solve an optimal shape design
problem in the similar way for diffusion systems involved with the initial,
boundary and terminal conditions so that the wished integral performance
criteria (defined on the domain and its boundary) be minimized. We remind that
Rubio in 1995 solved the similar optimal control problem by embedding method; he
also applied the Rudolph approach for getting better approximation. ? To be sure that the domain is simple in orthogonal coordinates, it is divided
into a fixed and a variable curves. Then by idea of approximating a curve with
broken lines and fixing the ycomponents, each admissible domain can be
represented with finite number of variables (domain variables). Therefore in the
first step of shapemeasure method, for a given domain, we will determine the
optimal control and the optimal value of objective function by applying the
obtained results from Rubio. Then a vector function on the set of admissible
domains will be set up in which it gives the optimal valve of objective function
for a given domain and its related optimal control function. Afterwards, in the
second step, by use of a standard minimization algorithm, the nearly optimal
domain and its related optimal control function will be determined at the same
time. Numerical examples will be also given. To get a better approximation, for the first time in optimal shape design problems, we may apply the GlashoffGustafson approach while Rubio used the Rudolph's one. 

Present Research Project at IPM 

Designing an Optimal Domain for a Diffusion Equation by Use of Measures  
Related Papers 
1.  A. Fakharzadeh Jahromi (Joint with J. E. Rubio) Best domain for an elliptic problem in Cartesian coordinates by means of shapemeasure Asian Journal of Control 11 (2009), 536547 [abstract] 
2.  A. Fakharzadeh J. Finding the optimum domain of a nonlinear wave optimal control system by measures J. Appl. Math. Comput. 13 (2003), 183194 [abstract] 
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