Zobrazeno 1 - 10
of 357
pro vyhledávání: '"Rocca, Elisabetta"'
In this paper, we tackle the problem of reconstructing earlier tumour configurations starting from a single spatial measurement at a later time. We describe the tumour evolution through a diffuse interface model coupling a Cahn-Hilliard-type equation
Externí odkaz:
http://arxiv.org/abs/2409.15925
The development of mathematical models of cancer informed by time-resolved measurements has enabled personalised predictions of tumour growth and treatment response. However, frequent cancer monitoring is rare, and many tumours are treated soon after
Externí odkaz:
http://arxiv.org/abs/2409.12844
In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the former, we ob
Externí odkaz:
http://arxiv.org/abs/2409.00528
Chemotaxis-inspired PDE model for airborne infectious disease transmission: analysis and simulations
Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics, with Fickian
Externí odkaz:
http://arxiv.org/abs/2404.17506
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer monitoring pr
Externí odkaz:
http://arxiv.org/abs/2404.12198
Autor:
Riva, Filippo, Rocca, Elisabetta
In this paper we consider two diffuse interface models for tumor growth coupling a Cahn-Hilliard type equation for the tumor phase parameter to a reaction-diffusion type equation for the nutrient. The models are distinguished by the presence of two d
Externí odkaz:
http://arxiv.org/abs/2402.19156
We consider the Oberbeck--Boussinesq approximation driven by an inhomogeneous temperature distribution on the boundary of a bounded fluid domain. The relevant boundary conditions are perturbed by a non--local term arising in the incompressible limit
Externí odkaz:
http://arxiv.org/abs/2402.06554
In this paper we study nonlocal-to-local asymptotics for a tumor-growth model coupling a viscous Cahn-Hilliard equation describing the tumor proportion with a reaction-diffusion equation for the nutrient phase parameter. First, we prove that solution
Externí odkaz:
http://arxiv.org/abs/2311.10457
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be shown constru
Externí odkaz:
http://arxiv.org/abs/2310.13601
In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial boundary va
Externí odkaz:
http://arxiv.org/abs/2309.09053