Abstract
The paper is devoted to studying a fourth order elliptic equation which has many applications in thin film theory and in the phase transformation theory. By using a truncation function method and a fixed point theorem, the existences of weak solutions and classic solutions for a steady state thin film equation are obtained respectively. Furthermore, the solutions also have positive lower bound. Finally, the viscosity vanishing limit is performed for positive solutions.
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Liang, B., Kong, L., Huang, F. (2014). Positive Steady State Solutions to a Nonlinear Fourth Order Elliptic Equation. In: Zhong, S. (eds) Proceedings of the 2012 International Conference on Cybernetics and Informatics. Lecture Notes in Electrical Engineering, vol 163. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3872-4_283
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DOI: https://doi.org/10.1007/978-1-4614-3872-4_283
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