Mathematics · Partial Differential Equations
Consider the one-dimensional heat equation ut = uxx for 0 0, with initial condition u(x, 0) = 2 cos2(πx) and boundary conditions ux(0, t) = 0, ux(1, t) = 0. The temperature distribution u(x, t) is given by:
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- 11 - e-4π2t sin(2πx)
- 21 + e-4π2t sin(2πx)
- 31 - e-4π2t cos(2πx)
- 41 + e-4π2t cos(2πx)✓
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1 + e-4π2t cos(2πx)
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