BLOW-UP SOLUTIONS TO THE NONLINEAR SECOND ORDER DIFFERENTIAL EQUATION u

The Space-Jump Model of the Movement of Tumor Cells and Healthy Cells

“…Now, the interaction of -cell and V-cell has been modelled. Model (14) will be used frequently in the following context, and some properties of two cell populations can be deduced from analyzing model (14). We show the analyzing procedures and some results in the next section.…”

“…We have got the system of PDEs (14) which shows the interaction of two cell populations. In this section, model (14) will be transformed to a system of o.d.es.…”

“…We have got the system of PDEs (14) which shows the interaction of two cell populations. In this section, model (14) will be transformed to a system of o.d.es. and then analyzed to obtain some properties of ]( , ) = ]( ) as approaches to zero and infinite; furthermore, the properties of ( , ) = ( ) will be deduced from the properties of ]( ) and ( ), where ( ) is ( ) + ]( ).…”

“…Our purpose is to obtain a simpler form of (14) in order to analyze the model conveniently. Supposing thatcell and V-cell have the same diffusion coefficient ( is equal to ] ), denotes the diffusion coefficients and ] .…”

“…Supposing thatcell and V-cell have the same diffusion coefficient ( is equal to ] ), denotes the diffusion coefficients and ] . Through changing variables, the system of PDEs (14) could be transformed to a system of o.d.es.…”