Long description: heatunstable
Alt text: A line graph showing the spatial profiles of three functions, \(u_j^0\), \(u_j\), and \(u_j^2\), versus the position \(x\) from zero to one.
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- The graph displays the concentration, denoted by \(u\), on the vertical axis, ranging from negative point five to zero point two five, plotted against the spatial coordinate \(x\) on the horizontal axis, from zero to one.
- Three distinct curves represent the functions: \(u_j^0\) (represented by circles and a solid line), \(u_j\) (represented by squares and a dashed line), and \(u_j^2\) (represented by stars and a dashed line).
- The function \(u_j^0\) starts at zero when \(x\) is zero, increases to its maximum value of approximately zero point two five at \(x = 0.5\), and decreases back to zero when \(x\) is one.
- The function \(u_j\) starts at zero when \(x\) is zero, rises to a small positive value of approximately zero point zero four at \(x = 0.5\), and decreases back to zero when \(x\) is one.
- The function \(u_j^2\) starts at zero when \(x\) is zero, increases to a peak of approximately zero point zero five at \(x = 0.5\), and then decreases back to zero when \(x\) is one.