New posts in partial-differential-equations

When does Separation of Variables yield basis of solution set?

functional-analysis partial-differential-equations

what is separation of variables

partial-differential-equations

Proving $\frac{200}{\pi}\sum_{n=0}^{\infty}\frac{(-1)^{n}}{(2n+1)\cosh\left(\frac{\pi}{2}(2n+1)\right)}=25$

calculus sequences-and-series partial-differential-equations summation

Why are weak solutions to PDEs good enough?

partial-differential-equations sobolev-spaces

$C^\infty_{0}(\bar\Omega)$ dense in $W^{k,p}(\Omega)$: the closure is necessary?

partial-differential-equations sobolev-spaces

Solving $uu_{x_1}+u_{x_2}=u$ with boundary conditions

partial-differential-equations characteristics

Maximum principle question for heat equation problem

partial-differential-equations heat-equation maximum-principle parabolic-pde

intuition behind weak solution

partial-differential-equations

cutoff function vs mollifiers

real-analysis partial-differential-equations sobolev-spaces distribution-theory regularity-theory-of-pdes

Fundamental Solution of the Four-Dimensional Laplacian

calculus real-analysis linear-algebra partial-differential-equations

General solution to the PDE $xU_x+yU_y=0$

partial-differential-equations

Upwind differencing scheme in Finite Volume Method (FVM)

partial-differential-equations numerical-methods finite-volume-method

Proof of Hartree Energy conservation

partial-differential-equations mathematical-physics calculus-of-variations euler-lagrange-equation

Burgers' equation $u_y + uu_x = 0$ with $u(x,0)=-x$

partial-differential-equations hyperbolic-equations

Positivity of principal eigenvalue for $L\phi=-\triangle \phi + \nabla \cdot( u \phi )$

partial-differential-equations eigenfunctions

Counter example of rellich-kondrachov compact embedding theorem on unbounded domain

functional-analysis partial-differential-equations sobolev-spaces

Why are elliptic/parabolic/hyperbolic PDEs called "elliptic"/"parabolic"/"hyperbolic"?

partial-differential-equations conic-sections

when does a separate-variable series solution exist for a PDE

partial-differential-equations

How to compute the first eigenvalue of Laplace operator in an ellipse?

ordinary-differential-equations eigenvalues-eigenvectors partial-differential-equations

Wave-Particle Duality in PDE?

ordinary-differential-equations reference-request partial-differential-equations physics intuition