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Publications [#347223] of Yuan Gao
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 Gao, Y, Global strong solution with BV derivatives to singular solidonsolid model with exponential nonlinearity,
Journal of Differential Equations, vol. 267 no. 7
(September, 2019),
pp. 44294447 [doi]
(last updated on 2022/05/25)
Abstract: In this work, we consider the one dimensional very singular fourthorder equation for solidonsolid model in attachmentdetachmentlimit regime with exponential nonlinearity ht=∇⋅([Formula presented]∇e [Formula presented])=∇⋅([Formula presented]∇e−∇⋅([Formula presented])) where total energy E=∫∇h is the total variation of h. Using a logarithmic correction for total energy E=∫∇hln∇hdx and gradient flow structure with a suitable defined functional, we prove the one dimensional evolution variational inequality solution preserves a positive gradient hx which has upper and lower bounds but in BV space. We also obtain the global strong solution to the solidonsolid model which allows an asymmetric singularity hxx+ to happen.


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