相关论文: Identifying early tumour states in a Cahn-Hilliard…
In this work, we develop a structure-preserving numerical scheme for a Cahn-Hilliard-Darcy model that describes tumor growth in a fluid-saturated porous medium. First, we derive a physically consistent model from the general framework…
In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalized and relaxed version…
We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and…
In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\mathcal{O} \subset \mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective…
A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…
The complex and dynamic crosstalk between tumour and immune cells results in tumours that can exhibit distinct qualitative behaviours - elimination, equilibrium, and escape - and intricate spatial patterns, yet share similar cell…
In this study, we model avascular tumour growth in epithelial tissue. This can help us to get a macroscopic view of the interaction between the tumour with its surrounding microenvironment and the physical changes within the tumour…
We analyse the Hamiltonian structure of a system of first-order ordinary differential equations used for modeling the interaction of an oncolytic virus with a tumour cell population. The analysis is based on the existence of a Jacobi Last…
We consider an evolutionary PDE system coupling the Cahn-Hilliard equation with singular potential, mass source and transport effects, to a Brinkman-type relation for the macroscopic velocity field and to a further equation describing the…
In this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport processes by an internal, non-solenoidal velocity field. We…
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…
Motivated by numerical simulations showing the emergence of either periodic or irregular patterns, we explore a mechanism of pattern formation arising in the processes described by a system of a single reaction-diffusion equation coupled…
In this contribution we show sufficient conditions for simultaneous unique identification of unknown spacewise coefficients and heat source in a parabolic partial differential equation given additional final time measurements. Our approach…
We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…
This paper introduces a method for estimating the shape and location of an embedded tumor. The approach utilizes shape optimization techniques, applying the coupled complex boundary method. By rewriting the problem -- characterized by a…