Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical un ....Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical understanding of which outflow shapes are stable, and under what circumstances they might become unstable. This will provide valuable information about galaxy shapes, and a new suite of computational methods for solving such problems.Read moreRead less
Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods f ....Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.
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Novel nonlinear functional analysis methods for singular and impulsive boundary value problems. This project aims to develop innovative functional analysis theories and methods to study various complex nonlinear boundary value problems, with particular focus on singular and impulsive problems. The outcomes of this project aims to enhance Australia’s capability of tackling complex nonlinear science and engineering problems using sophisticated mathematical methods. This project aims to also provid ....Novel nonlinear functional analysis methods for singular and impulsive boundary value problems. This project aims to develop innovative functional analysis theories and methods to study various complex nonlinear boundary value problems, with particular focus on singular and impulsive problems. The outcomes of this project aims to enhance Australia’s capability of tackling complex nonlinear science and engineering problems using sophisticated mathematical methods. This project aims to also provide engineers and scientists with a theoretical base and simulation technique for the study and optimal control of impulsive systems and processes involving nonlinear singularity.Read moreRead less