On a nonstandard problem for heat conduction in a cylinder

Abstract

Decay bounds are derived for the solution of a heat conduction problem in a semi-infinite cylinder when the lateral surface is held at zero temperature, a nonzero temperature is prescribed on the finite base, and the temperature at time T is prescribed to be a constant multiple of the temperature at initial time. Both energy and pointwise decay bounds are computed for a range of values of the constant multiple. Such problems were originally introduced as a means of stabilizing the backward-in-time problem for the heat equation.

Keywords:

• Heat conduction
• Nonstandard problem
• Decay bounds
• AMS Subject Classifications: Primary 35K05
• 35K20
• 35B30

Notes

^†E-mail: [email protected]

* E-mail: [email protected]

* E-mail: [email protected]

Additional information

Notes on contributors

P.W. Schaefer

†E-mail: [email protected] * E-mail: [email protected]