Bug introduced in 11.2 or earlier, fixed in 12.2 or earlier.
Reported to Wolfram with CASE number 4028951
on 11.3,
ClearAll[u,x,t];
eqn=D[u[x,t],t]+u[x,t]*D[u[x,t],x]==0;
bc=u[0,t]==0;
ic=u[x,0]==x;
sol=DSolve[{eqn,bc,ic},u[x,t],x,t]
What does, terms that have
DSolve`DsolveLaplaceTransformDump`
mean in the solution? It looks like DSolve starting using the Laplace method to solve the above PDE. But is the above answer meant to be the final answer, or did DSolve
gave up in the middle and these Dump
messages are left there?