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Creators/Authors contains: "Lu, Xin Yang"

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  1. ; ; (, SIAM Journal on Mathematical Analysis)
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  2. ; ; (, Journal of Nonlinear Science)
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  3. ; ; (, Interfaces and Free Boundaries)
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  4. ; ; (, Advances in Calculus of Variations)
    Abstract We study the following parabolic nonlocal 4-th order degenerate equation arising from the epitaxial growth on crystalline materials. Here a>0 is a given parameter. By relying on the theory of gradient flows,we first prove the global existence of a variational inequality solution with a general initial datum.Furthermore, to obtain a global strong solution, the main difficulty is the singularity of the logarithmic term when {u_{xx}+a} approaches zero. Thus we show that,if the initial datum is uniformly bounded away from zero,then such property is preserved for all positive times.Finally, we will prove several higher regularity results for this global strong solution.These finer properties provide a rigorous justification for the global-in-time monotone solution to the epitaxial growth model with nonlocal elastic effects on vicinal surface. 
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  5. ; ; (, SIAM Journal on Mathematical Analysis)
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  6. ; ; ; (, Modélisation mathématique et analyse numérique)
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  7. ; ; (, ESAIM: Control, Optimisation and Calculus of Variations)
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    In this work, we study a fourth order exponential equation, u t = Δ e −Δ u derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data. 
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  8. ; ; ; (, Calculus of Variations and Partial Differential Equations)
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