On Standard Eigenvalues of Variable-Coefficient Heat and Rod Equations
Keyword(s):
Forms of the variable-heat-conductivity coefficient function in the one-dimensional heat equation are determined which yield a standard harmonic eigenvalue sequence as in the case of homogeneity. The continuous case is found to correspond to a four-thirds power law dependence on coordinate. For the stepped case, the condition on the ratio of segmental heat conductivities in terms of the junction location is presented.
An alternative explicit expression of the kernel of the one dimensional heat equation with Dirichlet conditions
