Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term

Long Time Behavior for Solutions of the Diffusive Logistic Equation with Advection and Free Boundary

We consider the influence of a shifting environment and an advection on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is shifting and without advection (β = 0), Du, Wei and Zhou in [16] showed that the species always dies out when the shifting speed c∗ ≥ C, and the long-time behavior of the species is det...

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 rad...

Asymptotic Behavior of Energy Solutions to a Two Dimensional Semilinear Problem with Mixed Boundary Condition

Pergamon Asymptotic Behavior of Energy Solutions to a Two-dimensional Semilinear Problem with Mixed Boundary Condition

where: • f~ is a C °'1 and bounded domain in Rz; • 0f~ consists of two pieces F0 and F1, where the one-dimensional Hausdorff measure of F o is greater than 0; • F0 is smooth and F1 is piecewise smooth; • F0 and 1"1 are relatively closed in 0f~; • v is the unit outer normal of f~; • p is a large parameter. In this work, we shall only consider the least energy solutions, although the method can b...

Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-order Integral Boundary-value Problem

In this note, we extend the results by Jia et al [3] to a more general case. By refining the conditions imposed on f and finding more suitable upper and lower solution, we remove some key conditions used in [3], and still establish their results.