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Table 1 Some α , \(\pmb{\Vert u ( x,1;g ) - y ( x ) \Vert _{L_{2} ( 0,1 )}^{2}}\) and \(\pmb{\Vert g \Vert _{H^{1} ( 0,1 )}^{2}}\) values

From: On a Neumann boundary control in a parabolic system

α

\(\boldsymbol{\Vert u ( x,1;g ) - y ( x ) \Vert _{L_{2} ( 0,1 )}^{2}}\)

\(\boldsymbol{\Vert g \Vert _{H^{1} ( 0,1 )}^{2}}\)

0.001

0.025

25.610

0.05

0.088

23.032

0.1

0.241

20.941

0.4

2.077

13.014

0.6

3.563

10.003

0.8

5.004

7.927

1

6.337

6.438

2

11.318

2.881