Local well-posedness, global existence and blow-up for a heat equation with interior logarithmic source and nonlinear dynamic boundary condition

Abstract

In this article, a heat equation with an interior logarithmic source and a nonlinear dynamic boundary condition is considered. After establishing the local well-posedness, the global existence and finite time blow-up results of the solutions with different initial energy levels are given. Moreover, the lower bound of the maximal existence time of the weak solution is deduced for the special case m = 2.

Keywords

local well-posedness / global existence / blow-up / logarithmic nonlinearity source / nonlinear dynamic boundary condition

References

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