Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Hardy-Poincaré type inequalities derived from p-harmonic problems

100%

Skrzypczak I.

Banach Center Publications

2014

tom 101

nr 1

225-238

We apply general Hardy type inequalities, recently obtained by the author. As a consequence we obtain a family of Hardy-Poincaré inequalities with certain constants, contributing to the question about precise constants in such inequalities posed in [3]. We confirm optimality of some constants obtained in [3] and [8]. Furthermore, we give constants for generalized inequalities with the proof of their optimality.

Tumour angiogenesis model with variable vessels' effectiveness

63%

Poleszczuk J., Skrzypczak I.

Applicationes Mathematicae

2011

tom 38

nr 1

33-49

We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties of the proposed model and present some numerical simulations.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Banach Center Publications

2 Skrzypczak I.

1 Poleszczuk J.

1 2014

1 2011

Wyniki wyszukiwania

Hardy-Poincaré type inequalities derived from p-harmonic problems

Tumour angiogenesis model with variable vessels' effectiveness