Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction beten cell surface resident receptors and ligands present in the extra-cellular medium.  prove the existence and uniqueness of solutions.  also consider a number of biologically relevant asymptotic limits of the model.  prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface.  also report on numerical simulations illustrating convergence to one of the limiting problems as ll as the spatio-temporal distributions of the receptors and ligands in a realistic geometry.
['Charles M. Elliott', 'Thomas Ranner', 'Chandrasekhar Venkataraman']
I am writing a research paper on a idea Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics
[{"from": "human", "value": "I am writing a research paper on a idea Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction beten cell surface resident receptors and ligands present in the extra-cellular medium.  prove the existence and uniqueness of solutions.  also consider a number of biologically relevant asymptotic limits of the model.  prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface.  also report on numerical simulations illustrating convergence to one of the limiting problems as ll as the spatio-temporal distributions of the receptors and ligands in a realistic geometry."}]