Systems of Fully Nonlinear Parabolic Obstacle Problems with Neumann Boundary Conditions

• Published in: Applied mathematics & optimization Vol. 86; no. 2
• Main Authors: Lundström, Niklas L. P., Olofsson, Marcus
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-10-2022; Springer Nature B.V
• Subjects: Applied mathematics; Barrier; Barriers; Boundary conditions; Boundary value problems; Calculus of Variations and Optimal Control; Optimization; Constraints; Control; Fully nonlinear PDE; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Multi modes switching; Neumann boundary condition; Numerical and Computational Physics; Optimal switching; Optimization; Parabolic differential equations; Partial differential equations; Simulation; Stochastic models; Systems Theory; Theoretical; Viscosity; Viscosity solution; Fully nonlinear PDE; Optimal switching; Constraints; Viscosity solution; Multi modes switching; Neumann boundary condition; 35D40; Barrier; 35B50; 49L25; 35Q93
• ISSN: 0095-4616; 1432-0606; 1432-0606
• DOI: 10.1007/s00245-022-09890-z

We prove the existence of a unique viscosity solution to certain systems of fully nonlinear parabolic partial differential equations with interconnected obstacles in the setting of Neumann boundary conditions. The method of proof builds on the classical viscosity solution technique adapted to the setting of interconnected obstacles and construction of explicit viscosity sub- and supersolutions as bounds for Perron’s method. Our motivation stems from so called optimal switching problems on bounded domains.