5 papers
Renormalized Solution for the Nonlinear Parabolic Problem with Lower Order Terms
Shijun Li, Boai Huang, Shaopeng Xu
In this paper, we consider the following problem: \[ \begin{cases} -\nabla\cdot A(x,u,\nabla u) + H(x,u,\nabla u) = f(x), & x \in Ω, u = 0, & x \in \partial Ω, \end{cases} \] in…
Renormalized Solution for the Nonlinear Parabolic Problem with Lower Order Terms
Shijun Li, Shujing Li, Shaopeng Xu
In this paper, we consider the following nonlinear parabolic equation with non-coercive terms in \(R^N\) space \[ \dfrac{\partial u}{\partial t} -\nabla \cdot (a(x,t,u,\nabla u)+ Î…
Finite-time blow-up in a class of chemotaxis systems with spatially heterogeneous diffusion sensitivity
Yashuang Zhao, Shijun Li, Shaopeng Xu
\indent In this paper, we study a class of parabolic-elliptic Keller-Segel systems with diffusion sensitivity dependent on spatial position, given by type \begin{equation} \left\{…
Renormalized Solutions for a Class of Nonlinear Parabolic Equation with a Lower Order Term and Variable Exponents
Chunjin Li, Shijun Li, Shaopeng Xu
We consider a class of nonlinear parabolic equations \[ \dfrac{\partial}{\partial t} b(u)-\nabla \cdot (A(x,t,u,\nabla u))+H(x,t,\nabla u)=f , \] where is a nonlinear lower ord…
Approximation Analysis of a Parabolic-Parabolic Chemotaxis Model with Logarithmic Nonlinearity
Shijun Li, Yashuang Zhao, Shaopeng Xu +1
We consider the Keller-Segel system with logical source \begin{align*} \begin{cases} u_t = \nabla \cdot (Ï(u)\nabla u) - \nabla \cdot (Ï(u)\nabla v)+f(u), & x \in Ω, \; t > 0, v…