Positive Steady State Solutions to a Nonlinear Fourth Order Elliptic Equation
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.
KeywordsFourth order Steady state Higher order
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