In this paper we take up the question of analyticity properties of Dirichlet–Neumann operators with respect to boundary deformations. In two separate results, we show that if the deformation is… (More)

Mathematical models of tumor growth, which consider the tumor tissue as a density of proliferating cells, have been developed and studied in many papers; see [2,3,5–9,14,17–20] and the references… (More)

This paper studies the rst order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial di erential equations with pointwise state constraints. Pontryagin type… (More)

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive numbers ρ < R, there exists a… (More)

The growth of tumors can be modeled as a free boundary problem involving partial differential equations. We consider one such model and compute steady-state solutions for this model. These solutions… (More)

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive number R and 0 < ρ < R, there exists… (More)

Cell cycle is controlled at two restriction points, R (1) and R (2). At both points the cell will commit apoptosis if it detects irreparable damage. But at R (1) an undamaged cell also decides… (More)

Throughout this paper the normal n denotes the interior normal direction; i.e., n = ( f (x1); 1)= p 1 + jf (x1)j when x approaches from above (denoted by ) and n = (f (x1); 1)= p 1 + jf (x1)j from… (More)