We consider nonlinear evolution equations with logistic term satisfying initial Neumann-boundary condition and show global existence in time of solutions to the problem in arbitrary space dimension by using the method...We consider nonlinear evolution equations with logistic term satisfying initial Neumann-boundary condition and show global existence in time of solutions to the problem in arbitrary space dimension by using the method of energy. Applying the result to a mathematical model of tumour invasion, we discuss the property of the rigorous solution to the model. Finally we will show the time depending relationship and interaction between tumour cells, the surrounding tissue and matrix degradation enzymes in the model by computer simulations. It is seen that our mathematical result of the existence and asymptotic behaviour of solutions verifies our simulations, which also confirm the mathematical result visibly.展开更多
1 Results Recently much interest was focused on the indium chemistry. Barbier and, Reformatsky types of reactions are main streams of the chemistry. The synthetic application of indium hydride (HInCl2), however, has b...1 Results Recently much interest was focused on the indium chemistry. Barbier and, Reformatsky types of reactions are main streams of the chemistry. The synthetic application of indium hydride (HInCl2), however, has been just started in contrast to the chemistry of the same 13th group of elements such as aluminum and boron hydrides. At first we generated the hydride by the transmetallation between Bu3SnH and InCl3, and then found it has both considerable stability and reactivity, and the hydride could b...展开更多
文摘We consider nonlinear evolution equations with logistic term satisfying initial Neumann-boundary condition and show global existence in time of solutions to the problem in arbitrary space dimension by using the method of energy. Applying the result to a mathematical model of tumour invasion, we discuss the property of the rigorous solution to the model. Finally we will show the time depending relationship and interaction between tumour cells, the surrounding tissue and matrix degradation enzymes in the model by computer simulations. It is seen that our mathematical result of the existence and asymptotic behaviour of solutions verifies our simulations, which also confirm the mathematical result visibly.
文摘1 Results Recently much interest was focused on the indium chemistry. Barbier and, Reformatsky types of reactions are main streams of the chemistry. The synthetic application of indium hydride (HInCl2), however, has been just started in contrast to the chemistry of the same 13th group of elements such as aluminum and boron hydrides. At first we generated the hydride by the transmetallation between Bu3SnH and InCl3, and then found it has both considerable stability and reactivity, and the hydride could b...