9 research outputs found
A Global Attractivity in a Nonmonotone Age-Structured Model with Age Dependent Diffusion and Death Rates
In this paper, we investigated the global attractivity of the positive
constant steady state solution of the mature population governed by
the age-structured model: \begin{equation*} \left\{\begin{array}{ll}
\frac{\partial u}{\partial t}+\frac{\partial u}{\partial a}=D(a)\frac{\partial
^2 u}{\partial x^2} - d(a)u, & t\geq t_0\geq A_l,\;a\geq 0,\; 0< x< \pi,\\
w(t,x)=\int_r^{A_l}u(t,a,x)da,& t\geq t_0\geq A_l,\; 0<x<\pi,\\
u(t,0,x)=f(w(t,x)), & t\geq t_0\geq A_l,\; 0<x<\pi,\\
u_x(t,a,0)=u_x(t,a,\pi)=0,\;& t\geq t_0\geq A_l,\; a \geq 0, \end{array}
\right. \end{equation*} when the diffusion rate and the death rate
are age dependent, and when the birth function is nonmonotone. We
also presented some illustrative examples.Comment: 11 page
EXACTNESS OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS AND INTEGRATING FACTORS
Abstract. The principle of finding an integrating factor for a none exact differential equations is extended to equations of second order. If the second order equation is not exact, under certain conditions, an integrating factor exists that transforms it to an exact one. In this paper we give explicit forms for integrating factors of the second order differential equations
Age-structured population dynamics: age-dependent diffusion and death rates, and their applications to the cell population
Please see thesis for abstract