Abstract: | If the longitudinal line method is applied to the Cauchy problem ut = uxx, u(0, x) = u0(x) with a bounded function u0, one is led to a linear initial value problem v¢(t)=A v(t), v(0)=wv'(t)=A v(t),\, v(0)=w in l¥ (\Bbb Z)l^\infty (\Bbb Z). Using Banach limit techniques we study the asymptotic behaviour of the solutions of these problems as t tends to infinity. |