Pde Definition and 856 Threads

I'm working on solving coupled PDEs (mass diffusion - heat transfer - continuum mechanics) in problems where the solution domain changes depending on the solution (call it an intrinsic coupling if you will). This happens either due to addition of material to the domain or damage of the domain...

"Verify that, for any C¹ function f(x), u(x, t) = f(x - ct) is a solution of the PDE u_t + c u_x = 0, where c is a constant and u_t and u_x are partial derivatives." I managed to get the solution for this and a similar problem by showing that the new variable (x - ct in this case) satisfies...

I need your help, fellows ! I need the title and author of a good book on PDE. And also a good book with exercises on PDE. Can you help me, please ? :cry: regards Looker

du/dt = f(u)+D(laplacian*u) where u=u(x,y,t), D>0, f(u)=a*u I'm not sure where to start other than substitute f(u) with a*u. Suggestions?

Hi, I am quite new to the concept of stochastic equations. I am learning of it from some financial textbooks, however they lack a bit in the approach. Let me see if i understood Feynman-Kac: for every PDE in N dimensions (with second derivatives equivalent by unitary/orthogonal...

I have an assignment due at the end of the week, and I was wondering if someone could check my working for me, as I am prone to making errors. Also, in Step Five I am unsure how to solve for T(t), can anyone point me in the right direction? ∂u/∂t = (c/r)*(r(∂u/∂r)) +...