Chemotaxis-haptotaxis model of cancer invasion with tissue remodeling is one of the important PDE’s systems in medicine, mathematics and biomathematics. In this paper we find the solution of chemotaxis-haptotaxis mod...Chemotaxis-haptotaxis model of cancer invasion with tissue remodeling is one of the important PDE’s systems in medicine, mathematics and biomathematics. In this paper we find the solution of chemotaxis-haptotaxis model of cancer invasion using the new homotopy perturbation method (NHPM). Then by comparing some estimated numerical result with simulation laboratory result, it shows that NHPM is an efficient and exact way for solving cancer PDE’s system.展开更多
This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue. The model consists of three reaction- diffusion- taxis partial differential equations describing interactions between cancer cells, mat...This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue. The model consists of three reaction- diffusion- taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. The equation for cell density includes two bounded nonlinear density-dependent chemotactic and haptotactic sensitivity functions. In the absence of logistic damping, we prove the global existence of a unique classical solution to this model by some delicate a priori estimate展开更多
The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods.We assume that the equation ha...The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods.We assume that the equation has a hypothetical soliton solutions.By reorganizing the resulting equations,we obtain a system of equations.Using Maple software,we get unknown coefficients in the system and writing them in the original equation,we obtain new solition solutions of the equation.The results show that the soliton solutions generated by the method for the long and short-wave interaction system are bright,kink type,bright periodic and dark solutions.We provided 3-D figures to illustrate the solutions.Computational results indicate that the method employed in this paper is superior than some other methods used in the literature to solve the same system equations.展开更多
文摘Chemotaxis-haptotaxis model of cancer invasion with tissue remodeling is one of the important PDE’s systems in medicine, mathematics and biomathematics. In this paper we find the solution of chemotaxis-haptotaxis model of cancer invasion using the new homotopy perturbation method (NHPM). Then by comparing some estimated numerical result with simulation laboratory result, it shows that NHPM is an efficient and exact way for solving cancer PDE’s system.
文摘This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue. The model consists of three reaction- diffusion- taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. The equation for cell density includes two bounded nonlinear density-dependent chemotactic and haptotactic sensitivity functions. In the absence of logistic damping, we prove the global existence of a unique classical solution to this model by some delicate a priori estimate
文摘The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods.We assume that the equation has a hypothetical soliton solutions.By reorganizing the resulting equations,we obtain a system of equations.Using Maple software,we get unknown coefficients in the system and writing them in the original equation,we obtain new solition solutions of the equation.The results show that the soliton solutions generated by the method for the long and short-wave interaction system are bright,kink type,bright periodic and dark solutions.We provided 3-D figures to illustrate the solutions.Computational results indicate that the method employed in this paper is superior than some other methods used in the literature to solve the same system equations.
