Serge
Reputation
Top tag
Next privilege 250 Rep.
 Sep24 awarded Autobiographer Apr10 awarded Popular Question Nov3 accepted Stuck on Laplace's Equation Sep2 awarded Supporter Sep2 comment Stuck on Laplace's Equation Hi! Thank you very much for your answer. I don't have such a deep insight into PDEs, so it would really help to have a "rule" for it. From what I have understood, solutions are unique in every Laplace's Equation when its boundary conditions are $f(x,y)$? Would that be true for both Neumann and Dirichlet boundary conditions? So, can I even say that for every similar Laplace's Equation to this one, once I find a solution, it will be unique? That rule would apply to $\theta$, v and w in my problem, wouldn't it? Thank you! Sep2 asked Stuck on Laplace's Equation Aug23 comment Eigenvalue in Sturm-Liouville problem: why isn't this one valid? @Tunococ Hi, thank you very much. As you say, b is actually $\sqrt{\lambda-1}$. Now I see that it also has to be a real number. Thank you! Aug23 asked Eigenvalue in Sturm-Liouville problem: why isn't this one valid? Aug16 comment Drum membrane wave equation general solution (non-symmetrical) Hi @doraemonpaul, I alreade read that before posting but, even understanding it, I can't find why the solution in my notes works. In fact, when I try to do it I end up with something more similar to wikipedia's. Even so, I can't find the way to the radius equation here, while they should be equivalent. Aug15 asked Drum membrane wave equation general solution (non-symmetrical) Aug4 comment Wave Equation Neumann Boundary Conditions Thank you, timur! Aug4 comment Wave Equation Neumann Boundary Conditions Thank you very much! Aug4 awarded Scholar Aug4 accepted Wave Equation Neumann Boundary Conditions Aug4 comment Wave Equation Neumann Boundary Conditions thank you very much! As you said, I skipped that $\lambda=0$ solution. I just have a little question concerning the superposition of the solutions. Solving for $\lambda=0$ in both equations, I get that $X(x)=X_0$ and $T(t)=A_0t+B_0$ are solutions. Is it true that $u(x,t)=(A_0t+B_0)X_0$ is a solution for the problem? And then, thanks to linearity we can assume that $X_0=1$. Am I right? So finally we get the most general solution adding the ones for $\lambda>0$. Now that I have written this, it seems completely right. I think I was confusing when I should add or multiply solutions. Aug3 revised Wave Equation Neumann Boundary Conditions added 26 characters in body Aug3 comment Wave Equation Neumann Boundary Conditions @Valentin ...isn't it correct? I have also noticed that, when solving for $T(t)$, the solution assumes $T_0''=0$ so $T_0=A_0t+B_0$. I understand that, but I can't trace the origin of that $T_0''=0$ condition. Also, why should it be added instead of being included in the Fourier Series? Thank you very much. Aug3 comment Wave Equation Neumann Boundary Conditions @Valentin Hi, thank you very much. You are completely right, I made a mistake copying the BC. It's corrected now. About the eigenvalues, in all the exercises I've done, $\lambda_n$ is computed in the spatial equation and then substituted into the temporal one. Aug3 revised Wave Equation Neumann Boundary Conditions deleted 4 characters in body Aug3 awarded Student