Bound for heat equation solution in 1D – math.stackexchange.com
Guillermo García Sáez
Let $u$ solve the heat equation$$
u_t = u_{xx} \quad \text{in } (0,\pi)\times(0,\infty),$$
with Dirichlet boundary conditions
$$
u(0,t)=u(\pi,t)=0,$$
and initial data
$$
u(x,0)=f(x),
$$
where $f \in ...