hi can someone please help me to answer the following question:
Let u(x; t) be solution of heat equation ut - uxx = 0 x ∈ R; t > 0
u = g x ∈ R t = 0;
where g is twice dierentiable functions with compact support.
Let Sa(t) = {x ∈ R : ∖u(x; t)∖ > a} a set of x ∈ R where solution exceeds a.
Show that for any fixed a > 0 there exits 0 ≤T(a) < ∞ such that the set Sa(t) is empty.
thanks in advance
Let u(x; t) be solution of heat equation ut - uxx = 0 x ∈ R; t > 0
u = g x ∈ R t = 0;
where g is twice dierentiable functions with compact support.
Let Sa(t) = {x ∈ R : ∖u(x; t)∖ > a} a set of x ∈ R where solution exceeds a.
Show that for any fixed a > 0 there exits 0 ≤T(a) < ∞ such that the set Sa(t) is empty.
thanks in advance