Pde system Definition and 14 Threads

I know the method is involving adjoint equation, lagrange functional and conserwation laws but i dont know how to do it, please help! I know something like this: that we must split our function into two F=(F_1,F_2), also u=(u_1,u_2) and v=(v_1,v_2) and we must calculate adjoint equation F* and...

I have the following system of PDEs: \hat{\rho}\hat{c}_{th}\frac{\partial\hat{T}}{\partial\hat{x}}-\alpha_{1}\frac{\partial}{\partial\hat{x}}\left(\hat{k}(\hat{x})\frac{\partial\hat{T}}{\partial\hat{x}}\right)=\alpha_{1}\hat{\sigma}(\hat{x})\hat{E}...

To all who are interested in a source for the treatment of partial differential equations: Victor Ivrii, Toronto, Course notes, 310 pages https://www.ams.org/open-math-notes/omn-view-listing?listingId=110703&utm_content=buffer2458a&utm_medium=social&utm_source=facebook.com&utm_campaign=buffer

I have the code which solves the Sel'kov reaction-diffusion in MATLAB with a Crank-Nicholson scheme. I would love to modify or write a 2D Crank-Nicolson scheme which solves the equations: ##u_t = D_u(u_{xx}+u_{yy})-u+a*v+u^2*v## ##v_y = D_v(v_{xx}+v_{yy}) +b-av-u^2v## Where ##D_u, D_v## are...

Hi Forum, I'm trying to use Mathematica to graphically explore a system of four PDEs, as defined in Yang et al. (2002). Spatial Resonances and Superposition Patterns in a Reaction-Diffusion Model with Interacting Turing Modes. Physical Review Letters 88(20). The equations are: \frac{\partial...

(r^2 \nabla^2 - 1) X(r,\theta,z) + 2 \frac{\partial}{\partial \theta} Y(r,\theta,z) = 0 (r^2 \nabla^2 - 1) Y(r,\theta,z) - 2 \frac{\partial}{\partial \theta} X(r,\theta,z) = 0 any suggestions are greatly appreciated :)

All, I have a system of three coupled PDE and I discretized the equations using finite difference method. It results in a block matrix equations as: [A11 A12 A13] [x1] = [f1] [A21 A22 A23] [x2] = [f2] [A31 A32 A33] [x3] = [f3] where, any of Aij is a square matrix. I use...

All, As part of my research I came up with a boundary value problem where I need to solve the following system of coupled PDE: 1- a1 * f,xx + a2 * f,yy + a3 * g,xx + a4 * g,yy - a5 * f - a6 * g = 0 2- b1 * f,xx + b2 * f,yy + b3 * g,xx + b4 * g,yy - b5 * f - b6 * g = 0 Where, ai's...

Hi all! I'm stuck with a system of PDE. I'm not sure I want to write it here in full, so l'll write just one of them. I've found a solution to this equation but I'm not sure it's the most general one since when I plug this solution into the other eqs, I get a trivility condition for the...

Hi all, I have a system of 3 coupled linear PDEs which can be expressed in matrix form as: \left( \begin{array}{ccc} \alpha_1 \partial_{\theta} & \alpha_2 & \alpha_3 \\ \beta_1 \partial_r & \beta_2 & \beta_3 \\ 0 & \gamma_2 \partial_{\theta} & 1 + \gamma_3 \partial_r \\ \end{array}...

Hi everyone! I want to design a robust controller for a system which is driven by a PDE. I need to acquire its transfer function in 's' parameter which means it should be transferred by Laplace transformation. I know that the result transfer function will be an infinite series of transfer...

Hi all, I am looking for ways to solve the following system of equations for \vec{B}: \vec{B} \cdot \nabla f = 0 \left( \nabla \times \vec{B} \right) \cdot \nabla f = 0 \nabla \cdot \vec{B} = 0 and f is a known scalar function. I think we can assume there is a solution since we...

Dear All, I am trying to solve the following system of PDEs \frac{\partial{A}}{\partial{t}}= a_{2}\frac{\partial{{^{2}}A}}{\partial{x^{2}}}-a_{1}\frac{\partial{A}}{\partial{x}}-a_{0}A+b_{0}B \frac{\partial{B}}{\partial{t}}=...

Hi Solving a Killing vector problem, in General Relativity, I got the following PDE system: \frac{\partial X^0}{\partial x}=0 \frac{\partial X^1}{\partial y}=0 \frac{\partial X^2}{\partial z}=0 \frac{\partial X^0}{\partial y} + \frac{\partial X^1}{\partial x}=0 \frac{\partial...