arXiv subjects

Junde Wu

Publications and source records attributed to Junde Wu.

147 records · Page 9Linked to original sources

arXiv2011

Samuel multiplicities and Browder Spectrum of Operator Matrices

we show that the definitions of some classes of semi-Fredholm operators, which use the language of algebra and first introduced by X. Fang in [8], are equivalent to that of some well-known operator classes. For example, the concept of shift-like semi-Fredholm operator on Hilbert space coincide with that of upper semi-Browder operator. For applications of Samuel multiplicities we characterize the sets of $\bigcap_{C\in B(K,\,H)}σ_{ab}(M_{C}),\bigcap_{C\in B(K,\,H)}σ_{sb}(M_{C})$ and $\bigcap_{C\in B(K,\,H)}σ_{b}(M_{C}),$ respectively, where $M_{C}=({array}{cc}A&C 0&B {array})$ denotes a 2-by-2 upper triangular operator matrix acting on the Hilbert space $H\oplus K$.

math.FA↗

arXiv2008

Asymptotic Stability of Stationary Solutions of a Free Boundary Problem Modeling the Growth of Tumors with Fluid Tissues

This paper aims at proving asymptotic stability of the radial stationary solution of a free boundary problem modeling the growth of nonnecrotic tumors with fluid-like tissues. In a previous paper we considered the case where the nutrient concentration $σ$ satisfies the stationary diffusion equation $Δσ=f(σ)$, and proved that there exists a threshold value $γ_*>0$ for the surface tension coefficient $γ$, such that the radial stationary solution is asymptotically stable in case $γ>γ_*$, while unstable in case $γ<γ_*$. In this paper we extend this result to the case where $σ$ satisfies the non-stationary diffusion equation $\epsln\partial_tσ=Δσ-f(σ)$. We prove that for the same threshold value $γ_*$ as above, for every $γ>γ_*$ there is a corresponding constant $\epsln_0(γ)>0$ such that for any $0<\epsln<\epsln_0(γ)$ the radial stationary solution is asymptotically stable with respect to small enough non-radial perturbations, while for $0<γ<γ_*$ and $\epsln$ sufficiently small it is unstable under non-radial perturbations.

math.AP↗

arXiv2008

Asymptotic Behavior of Solutions of a Free Boundary Problem Modelling the Growth of Tumors with Stokes Equations

We study a free boundary problem modelling the growth of non-necrotic tumors with fluid-like tissues. The fluid velocity satisfies Stokes equations with a source determined by the proliferation rate of tumor cells which depends on the concentration of nutrients, subject to a boundary condition with stress tensor effected by surface tension. It is easy to prove that this problem has a unique radially symmetric stationary solution. By using a functional approach, we prove that there exists a threshold value $γ_*>0$ for the surface tension coefficient $γ$, such that in the case $γ>γ_*$ this radially symmetric stationary solution is asymptotically stable under small non-radial perturbations, whereas in the opposite case it is unstable.

math.AP↗