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Article Contents

# Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach

• In this article, we continue the study of viscosity solutions for second-order fully nonlinear parabolic equations, having a $L^1$ dependence in time, associated with nonlinear Neumann boundary conditions, which started in a previous paper (cf [2]). First, we obtain the existence of continuous viscosity solutions by adapting Perron's method and using the comparison results obtained in [2]. Then, we apply these existence and comparison results to the study of the level-set approach for front propagations problems when the normal velocity has a $L^1$-dependence in time.
Mathematics Subject Classification: Primary: 35K60, 49L25 ; Secondary: 35B05.

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