Mathematical theory for epitaxial growth of thin films
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Affiliation:
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Xiangsheng Xu
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Mississippi State University
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USA
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Introduction:
| | Epitaxial growth of thin films is an important process in which new crystal materials are fabricated. It is a cornerstone of modern materials science, enabling tailored crystal structures for electronics, photonics, and nanotechnology. Mathematical modeling of the process leads to fourth-order parabolic equation with exponential non-linearity. Mathematical analysis encounters many challenges. The most prominent one is that the maximum principle is no longer true for fourth-order parabolic equations. Furthermore, it is very difficult to obtain a priori estimates for the exponent terms in the equations. The objective of the session is to exchange ideas on how to deal with these and other related issues.
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