All Questions

In a try to solve a physical problem, I've faced a system of first-order partial differential equations of the form $$\cos\left(t\right)\partial_{x}\mathbf{u}+\sin\left(t\right)\partial_{y}\mathbf{u}+...

I asked the question on math.stackexchange.com, but didn't get any reply. So, I asked it again here. Any suggestion or hint is welcome, and thank you for your attention. Consider the system of first ...

Let $f$ be a smooth function on $R^2$, and define $N_f$ to be the set of points $p$ such that the nodal set of $f$ ($\{x\in R^2: f(x)=0\}$) divided every neighborhood of $p$ into four regions. Indeed, ...

I would like to obtain analytic solutions to the following PDE system: \begin{equation} \rho_t + D(\lambda)\,\rho_\lambda = A(\lambda) \rho, \tag{1} \end{equation} with $\rho = (\rho_0,\rho_1)^T$, $D$ ...

I am working with this system of first order PDEs: \begin{equation} \left\{ \begin{aligned} %Suscettibili &\frac{\partial{S}(a,t)}{\partial{t}} + \frac{\partial{S}(a,t)}{\partial{a}}= -\lambda(a,...