I am trying to solve following PDE using DSolve but there is no result upon completion-

DSolve[D[-A[r,t],t]D[A[r,t],r]+A[r,t]D[D[A[r,t],r],t]==0,A[r, t], {r, t}]
  • $\begingroup$ DSolve[]'s support for PDE's is still somewhat limited, so don't be surprised if some things don't work yet :P. Try alternative -> Maple. $\endgroup$ – Mariusz Iwaniuk Feb 9 '18 at 12:59
  • $\begingroup$ The approach A[r,t]=R[r]T[t](separation of variables) solves the pde without any restriction concerning R[r],T[t] ??? $\endgroup$ – Ulrich Neumann Feb 9 '18 at 13:04

Your pde leads to $1=1$. So any two random functions $R(r)$ and $T(t)$ give a solution.

Solve $$ -u_{t}u_{r}+u\ u_{rt}=0 $$

Let $u=R\left( r\right) T\left( t\right) $ then the above becomes

\begin{align*} -\left( RT^{\prime}\right) \left( R^{\prime}T\right) +\left( RT\right) \ \left( R^{\prime}T^{\prime}\right) & =0\\ R^{\prime}T^{\prime} & =R^{\prime}T^{\prime}\\ 1 & =1 \end{align*}

So try any random functions, $R(r)$ and $T(t)$, they will be a solution

   u=R0 T0;     
   Simplify[D[-u,t]D[u,r]+u D[D[u,r],t]]

 (* 0 *)

 (* 0 *)

 solvePDE[r^3, t^8, r, t]
 (* 0 *)

May be Mathematica should just have returned $F1(r) F2(t)$ as an answer?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.