The possibility of a blow-up solution to the heat equation with a concentrated source in a finite strip is examined. It is found that blow-up always occurs for the Neumann problem, whereas for the Dirichlet problem it depends upon the length of the strip and proximity of the source site to the boundary. For those situations in which blow-up does occur, the growth rate is determined for a certain class of nonlinearities.
|Journal||Methods and Applications of Analysis|
|State||Published - 1994|