New posts in Partial Differential Equations

Impose PDE itself as Boundary Condition?

Smoothness of quotient of Holder continuous functions, provided the decay

Another second order PDE in canonical form

Why does separation of variable gives the general solution to a PDE

$\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}$ with $u(x,0)=\frac{e^{2x}-1}{e^{2x}+1}$. Then $\lim_{t \to \infty}u(1,t)$ equals

Show that the sum of a function series is bounded

Heat PDE with unusual, inhomogeneous Neumann boundary condition

Variant of parabolic maximum principle: $\partial_t u\ge \Delta_x u + b\cdot\nabla_x u-u \;\Rightarrow\; u\ge e^{-t}\inf_y u(0,y)$

Is there a reason it is so rare we can solve differential equations?

Finding the solution of $u_x + y u_y = 0$ using $u(0, y) = y^3$