If we have $$u_t + u_x =f(x,t)$$ with initial boundary conditions $u(0,t)=0$ for $t>0$ and $u(x,0)=0$ for $0
Can anyone tell me how to prove the stability estimate $$\int_0^r (u(x,t))^2 dx \leq e^t \int_0^t \int_0^R f^2(x,s)dx ds$$ where $t>0$
If we have $$u_t + u_x =f(x,t)$$ with initial boundary conditions $u(0,t)=0$ for $t>0$ and $u(x,0)=0$ for $0
Can anyone tell me how to prove the stability estimate $$\int_0^r (u(x,t))^2 dx \leq e^t \int_0^t \int_0^R f^2(x,s)dx ds$$ where $t>0$