Smooth Examples Solutions .Burgers Equation Consider the initial data c<0 (a,0)={1-m0≤c≤1 c>1 SMA-HPC⊙2003MT Hyperbolic Equations 15
Smooth Examples Solutions .Burgers Equation 0 1-a 0 t SMA-HPC⊙2003MT Hyperbolic Equations 16
Smooth Examples Solutions .Burgers Equation For t< 1 d Forest: dt=1+a=t+ ao u(a, t)=1 Fort<a<i: da 1-c0→}m=(1-o)t+m u(,t)=1-o= 1-t For x> 1 d=0→c=0→u(m,+)=0 SMA-HPC⊙2003MT Hyperbolic Equations 17
Smooth EXamples Solutions Burgers' Equation u(m,1/2) For t=1 u (C,0 ∫1c<1 (a4t)三 0c>1 The procedure breaks down for t> 1 SMA-HPC⊙2003MT Hyperbolic Equations 18