We consider boundary conditions (self-adjoint extensions) corresponding to point-like interactions for one-dimensional Dirac operator. Taking the non-relativistic limit we show how all possible point-like interactions for one-dimensional Schrödinger operator of free spinless particle can be obtained from the Dirac Hamiltonian. In case of spin-1/2 we show that there are boundary conditions with...
We examine the tumour growth model proposed in [1]. In the 2D case, the governing equations after some simplifications take the form
$\begin{array} {l}
\alpha_t + \left(\alpha u^1\right){x}+\left(\alpha u^2\right){y}=
S(\alpha), \
u^1_{x} + u^2_{y} = \nabla\cdot\left(D(\alpha)\nabla p\right), \
\Big[(2+\lambda)\alpha u^1_{x} + \lambda \alpha u^2_{y}\Big]x + \Big[\alpha u^1{y} +...