The solution of equation (13) of the form h(x, t)=u(t) θ(x) (i.e. in separating variables) is ca

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Step 1:u000ALetu0027s start by substituting the separated form $h(x,t) u003D u(t)u005Ctheta(x)$ into equation (1

The solution of equation (13) of the form $h(x, t)=u(t) \theta(x)$ (i.e. in separating variables) is called regular regime of Bussinesque in the case $u(t) \rightarrow 0, t \rightarrow \infty$. Show that $u(t)$ is a power function of time at large $t$.