New posts in Partial Differential Equations

solution to a general integral $\int_0^\infty \frac{\cos(tx)}{x^2+k^2}e^{-sx}dx$

Explain why the characteristic curves generate the solution surface

A Hamiltonian inequality using uniform convexity and Taylor's formula (Evans PDE, §3.3.3, Lemma 4, (36))

Solving the "Transport" PDE in the sense of distributions with Dirac Delta Source

Why are certain PDE called "elliptic", "hyperbolic", or "parabolic"?

Why is there no harmonic function on compact Riemannian manifold?

How to find the conserved quantities of $\phi^4$ model?

Is there a coordinate-free definition of a differential operator?

PDE, wave equation and energy function.

Solving the PDE $x_{1}\dfrac{\partial f}{\partial x_{1}}+x_{2}\dfrac{\partial f}{\partial x_{2}}=e^{f(x_{1},x_{2})}-\alpha.$