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\section*{List of Figures}
\begin{description}
\item[Figure 1:]
One-dimensional solutions to the nonlinear
density-dependent diffusion-convection equation
(\ref{eq:w1})--(\ref{eq:nlfn}) are shown schematically.
(a) A heterogeneous steady-state solution is shown for $\alpha=1/2$ (see
(\ref{eq:w1_sol}).
(b) A radially expanding solution is
shown for $c_u=0$ (porous media equation) (see (\ref{eq:pm_1d})).
\item[Figure 2:]
Numerical solution to the time-dependent problem achieves a steady-state
solution for large time. Shown is the solution to the time-dependent
problem:
(\ref{eq:w1a})--(\ref{eq:w2a}),
(\ref{eq:w1_zf})--(\ref{eq:w2_zf}), (\ref{eq:ics_1}) and
(\ref{eq:p1a})--(\ref{eq:q1a}), (\ref{eq:symm}),
(\ref{eq:org_cent}), (\ref{eq:cdef}), $a(w)=0$, $d(w)=d$, $b(w)=0$,
and $\mu=0$ for $t=??$. Initial conditions are given by (\ref{eq:H_ic}).
The Method of Lines and Gear's Method were used to solve the system.
\item[Figure 3:]
The analytical solution to (\ref{eq:asin_u})--(\ref{eq:asin_v}) is given
by (\ref{eq:vsol_asin}). The solution is shown here for $b=?$, $c=?$ and
$d=?$.
\item[Figure 4:]
The analytical solution to (\ref{eq:v_fun}), (\ref{eq:gam1_cons})
for $E=1$ is given by (\ref{eq:v_expl}). Solutions are shown here for the
values given in Table 1, with $\mu$ varying from $0.42$ (shallow curve) to
$0.48$ (steep curve).
\item[Figure 5:]
Cumulative wolf-pack densities $u(x)+v(x)$ and cumulative RLU densities
$p(x)+q(x)$ were calculated using (\ref{eq:v_expl}), $u=v(1-x)$,
(\ref{eq:p_ss}) and $q=p(1-x)$. The values for $\mu$ is $\mu=0.48$ and
the values for $v(0)$ and $c/d$ are taken from Table 1.
Note that the cumulative pack density decreases
and cumulative RLU density increases near $x=1/2$.
\item[Figure 6:]
A numerical solution the time-dependent problem
achieves a steady-state solution for large time
Shown is the solution to the time-dependent problem:
(\ref{eq:w1a})--(\ref{eq:w2a}),
(\ref{eq:w1_zf})--(\ref{eq:w2_zf}), (\ref{eq:ics_1}) and
(\ref{eq:p1a})--(\ref{eq:q1a}), (\ref{eq:symm}),
(\ref{eq:org_cent}), (\ref{eq:cdef}), $a(w)=0$ and $b(w)=0$
for the $\mu=0.48$ case from Table 1
($c=1$ and $d=1/7.3584$) for $t=??$.
Initial conditions were given by (\ref{eq:H_ic}).
The Method of Lines and Gear's Method were used to solve the system.
\item[Figure 7:]
A numerical solution the time-dependent problem
achieves a steady-state solution for large time
Shown is the solution to the time-dependent problem:
(\ref{eq:w1a})--(\ref{eq:w2a}),
(\ref{eq:w1_zf})--(\ref{eq:w2_zf}), (\ref{eq:ics_1}) and
(\ref{eq:p1a})--(\ref{eq:q1a}), (\ref{eq:symm}),
(\ref{eq:org_cent}), (\ref{eq:cdef}), $a(w)=0$ and $b(w)=0$
for the case $\mu=1.1$, $c=1$, $d=0.3$.
Initial conditions were given by (\ref{eq:H_ic}).
(a) Profiles for $u(x)$, $v(x)$, $p(x)$ and $q(x)$.
Note that both $p(x)$ and $q(x)$ have interior maximums near
the point $x=1/2$.
(b) Profiles for $u(x)$, $v(x)$, the cumulative wolf pack density
($u(x)+v(x)$), and $E+1=\exp(\mu k)=(1+\mu u(x))(1+\mu v(x))$.
Note that the cumulative wolf pack density is lowest at $x=1/2$,
and $E+1$ is constant across the domain.
The Method of Lines and Gear's Method were used to solve the system.
\end{description}