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Explicit phase diagram for a one-dimensional blister model

In this article, we consider a simple one-dimensional variational model, describing the delamination of thin films under cooling. We characterize the global minimizers, which correspond to films of three possible types: non delaminated, partially delaminated (called blisters), or fully delaminated. Two parameters play an important role: the length of the film and the cooling parameter. In the phase plane of those two parameters, we classify all the minimizers. As a consequence of our analysis, we identify explicitly the smallest possible blisters for this model.