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Global strong solution with BV derivatives to singular solid-on-solid model with exponential nonlinearity
- Source :
- Journal of Differential Equations. 267:4429-4447
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity $$h_t = \nabla \cdot (\frac{1}{|\nabla h|} \nabla e^{\frac{\delta E}{\delta h}}) =\nabla \cdot (\frac{1}{|\nabla h|}\nabla e^{- \nabla \cdot (\frac{\nabla h}{|\nabla h|})})$$ where total energy $E=\int |\nabla h|$ is the total variation of $h$. Using a logarithmic correction $E=\int |\nabla h|\ln|\nabla h| d x$ and gradient flow structure with a suitable defined functional, we prove the evolution variational inequality solution preserves a positive gradient $h_x$ which has upper and lower bounds but in BV space. We also obtain the global strong solution to the solid-on-solid model which allows an asymmetric singularity $h_{xx}^+$ happens.<br />Comment: 15 pages
- Subjects :
- Work (thermodynamics)
Logarithm
Applied Mathematics
010102 general mathematics
Mathematics::Analysis of PDEs
Space (mathematics)
01 natural sciences
Upper and lower bounds
010101 applied mathematics
Mathematics - Analysis of PDEs
Singularity
Variational inequality
Radon measure
FOS: Mathematics
0101 mathematics
Balanced flow
Analysis
Analysis of PDEs (math.AP)
Mathematical physics
Mathematics
Subjects
Details
- ISSN :
- 00220396
- Volume :
- 267
- Database :
- OpenAIRE
- Journal :
- Journal of Differential Equations
- Accession number :
- edsair.doi.dedup.....2209570740542153a9d243f1e2e535e2