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Abstract
We study here a singular perturbation problem of biLaplacian type, which can be seen as the biharmonic counterpart of classical combustion models. We provide different results, that include the convergence to a free boundary problem driven by a biharmonic operator, as introduced in Dipierro et al. (arXiv:1808.07696, 2018), and a monotonicity formula in the plane. For the latter result, an important tool is provided by an integral identity that is satisfied by solutions of the singular perturbation problem. We also investigate the quadratic behaviour of solutions near the zero level set, at least for small values of the perturbation parameter. Some counterexamples to the uniform regularity are also provided if one does not impose some structural assumptions on the forcing term.
Original language  English 

Pages (fromto)  679713 
Journal  Applied Mathematics and Optimization 
Volume  80 
Issue number  3 
DOIs  
Publication status  Published  1 Dec 2019 
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Partial Differential Equations, free boundaries and applications
30/11/18 → 30/11/22
Project: Research
