相关论文: Free boundary regularity for tumor growth with nut…

We extend basic regularity of the free boundary of the obstacle problem to some classes of heterogeneous quasilinear elliptic operators with variable growth that includes, in particular, the $p(x)$-Laplacian. Under the assumption of…

We study the behavior of solutions to the first-order mean field games system with a local coupling, when the initial density is a compactly supported function on the real line. Our results show that the solution is smooth in regions where…

Accurately modeling the spatiotemporal evolution of tumor morphology from baseline imaging is a pre-requisite for developing digital twin frameworks that can simulate disease progression and treatment response. Most existing approaches…

We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We find that invasion into the cancer-free state may be…

A class of diffusion driven Free Boundary Problems is considered which is characterized by the initial onset of a phase and by an explicit kinematic condition for the evolution of the free boundary. By a domain fixing change of variables it…

In this paper we study asymptotic behavior of solutions for a multidimensional free boundary problem modelling the growth of nonnecrotic tumors. We first establish a general result for differential equations in Banach spaces possessing a…

Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis.…

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney & Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell…

We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term…

In this paper we study the "stiff pressure limit" of the porous medium equation, where the initial density is a bounded, integrable function with a sufficient decay at infinity. Our particular model, introduced by Perthame-Quiros-Vazquez,…

In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death…

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…

In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting…

In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations…

We study an equation structured by age and a phenotypic trait describing the growth process of a population subject to aging, competition between individuals, and mutations. This leads to a renewal equation which occurs in many evolutionary…

A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a convective Cahn-Hilliard equation for the evolution of the tumour to a reaction-diffusion-advection…

Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the…

We analyze a system of cross-diffusion equations that models the growth of an avascular-tumor spheroid. The model incorporates two nonlinear diffusion effects, degeneracy type and super diffusion. We prove the global existence of weak…

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…

Complex tumor-host interactions can significantly affect the growth dynamics and morphologies of progressing neoplasms. The growth of a confined solid tumor induces mechanical pressure and deformation of the surrounding microenvironment,…