Identification of the initial temperature from the given temperature data at the left end of a rod

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Dec 18, 2019

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α	$\begin{matrix} {∥u (0, t;; v) - e^{t}∥}_{L_{2} (0, 1)}^{2} \end{matrix}$ $\begin{array}{} \displaystyle {\left\\|{\mathbf u}\left({\mathbf 0},{\mathbf t};;{\mathbf v}\right){\mathbf -}{{\mathbf e}}^{{\mathbf t}}\right\\|}^{{\mathbf \, }{\mathbf 2}}_{{{\mathbf L}}_{{\mathbf 2}}\left({\mathbf 0},{\mathbf 1}\right)} \end{array}$	$\begin{matrix} {∥v∥}_{L_{2} (0, 1)}^{2} \end{matrix}$ $\begin{array}{} \displaystyle {\left\\|{\mathbf v}\right\\|}^{{\mathbf 2}}_{{{\mathbf L}}_{{\mathbf 2}}\left({\mathbf 0},{\mathbf 1}\right)} \end{array}$
0.1	0.02703	0.20904
0.2	0.03356	0.18194
0.3	0.04015	0.16205
0.4	0.04673	0.14153
0.5	0.05348	0.12598
1.0	0.08095	0.07398
2.0	0.11747	0.03282

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Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other