Abstract
In the paper, we study a fourth order partial differential equation which appears in the description of the motion of a very thin layer of viscous incompressible fluids and in the phase transformation theory. In order to prove the existence, a truncation system is studied. By applying the test function method and an iteration technique, some a-prior estimates of solutions to the steady state problem are obtained. Finally, the boundedness estimates are gained for the truncation problem. The results will have important in the existence of steady state thin film equations.
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Liang, B., Dai, X., Wang, M. (2014). Boundedness Estimates to a Steady State 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_197
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DOI: https://doi.org/10.1007/978-1-4614-3872-4_197
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