Abstract. A property of the maximum temperature corresponding to certain family of heat-conduction problems with boundary condition of flux-temperature type is discussed in this paper. This peoperty states the maximum temperature attains a maximum value when the flux condition is prescibed on a connected portion of the boundary. For a semi-infinite plate the property is rigorously established while it is conjectured to hold for every convex and bounded domain.
1991 Mathematics Subject Classification. 35K05, 35B99, 49K20.
Key words and phrases. Heat equation, mixed initial boundary value problem, maximum temperature.