The time-dependent diffusion equation: An inverse diffusivity problem
نویسندگان
1 School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran.
2 School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran.
3 School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran.
4 School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran.
5 School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran.
doi
10.22067/ijnao.2021.11309.0چکیده
We find a solution of an unknown time-dependent diffusivity a(t) in a linear inverse parabolic problem by a modified genetic algorithm. At first, it is shown that under certain conditions of data, there exists at least one solution for unknown a(t) in (a(t), T (x, t)), which is a solution to the corresponding problem. Then, an optimal estimation for unknown a(t) is found by applying the least-squares method and a modified genetic algo rithm. Results show that an excellent estimation can be obtained by the implementation of a modified real-valued genetic algorithm within an Intel Pentium (R) dual-core CPU with a clock speed of 2.4 GHz.
