The Green function has played a key role in the analytical approach that in recent years has led to important developments in the study of stochastic processes with jumps. In this Research Note, the authors-both regarded as leading experts in the field- collect several useful results derived from the construction of the Green function and its estim
This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.
The Green function has played a key role in the analytical approach that in recent years has led to important developments in the study of stochastic processes with jumps. In this Research Note, the authors-both regarded as leading experts in the field- collect several useful results derived from the construction of the Green function and its estimates. The first three chapters form the foundation for the rest of the book, presenting key results and background in integro-differential operators, and integro-differential equations. After a summary of the properties relative to the Green function for second-order parabolic integro-differential operators, the authors explore important applications, paying particular attention to integro-differential problems with oblique boundary conditions. They show the existence and uniqueness of the invariant measure by means of the Green function, which then allows a detailed study of ergodic stopping time and control problems.
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