<p style='text-indent:20px;'>We are concerned with bifurcation diagrams of stationary solutions to a phase field model proposed by Fix and followed by Caginalp. We show all the global bifurcation diagrams of stationary solutions to the model in the 1-dimension case. We see that bifurcation diagrams are surprisingly rich in variety depending on the latent heat and the initial total enthalpy. For instance, bifurcation diagrams include the secondary bifurcation point where symmetric breaking occurs, and curves which connect a limit of boundary layer solutions to the other limit of internal layer solutions.</p>
<abstract> <p>This paper presents a mathematical model governing the dynamics of a morphogenetic vascular endothelial cell (EC) during angiogenesis, and vascular growth formed by EC. Especially, we adopt a multiparticle system for modeling these cells. This model does not distinguish a tip cell from a stalk cell. A formed vessel is modeled using phase-field equation to prevent capillary expansion with time stepping in particular. Numerical simulation reveals that all cells are moving in the direction of high concentration of vascular endothelial growth factor (VEGF), and that they are mutually repellent in cases in which they are closer than some threshold.</p> </abstract>