Questions on "Partial Differential Equations", as opposed to "ordinary differential equations".

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2
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5answers
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Proving unique weak solution.

I am attempting to solve some problems from Evans , I need some help with the following question. If $u\in H^2_0\Omega$, where $\Omega$ is open, bounded subset of $R^n$. How can i solve biharmonic ...
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1answer
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How do I solve an inhomogeneous Helmholtz boundary value problem in 2-D with a rectangular boundary?

I need to solve the following BVP: $\Delta u - 1/\delta * u = R(x,y)$, where $\Delta$ is the laplacian operator. and boundary conditions: $u(0,y)=u(L,y)=u(x,0)=u(x,L)=0$ where $L=1$, ...
2
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0answers
81 views
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numerical method (implicit , backward difference or forward difference) for nonlinear pde

$\newcommand{\lbar}{\underline{\lambda}}$ In this linear PDE: \begin{cases} B_t+b^Q(r,t)B_r+\frac{1}{2}d^2(r,t)B_{rr}+(\mu(\lambda,t)+\alpha \sigma (t))(\lambda -\lbar)B_{\lambda} \\ ...