Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition

This paper deals with a class of heat emission processes in a medium with a nonegative source, a nonlinear decreasing thermal conductivity and a linear radiation (Robin) boundary condition. For such heat emission problems, using a differential inequality technique, we establish conditions on the data sufficient to guarantee that the blow-up of the solutions does occur or does not occur. In addition, the same technique is used to determine a lower bound for blow-up time blow-up occurs. AMS Classification: Primary 35K20, 35B40; Secondary 35B45.