Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 1004

Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

56 votes
Accepted

Unconditional nonexistence for the heat equation with rapidly growing data?

It is true that for any initial datum $u_0\in C^\infty(\mathbb{R})$ there exists a solution $u\in C^\infty(\mathbb{R}^+\times\mathbb{R})$ to the heat equation with initial condition $u(0,x)=u_0(x)$. A …
SBF's user avatar
  • 1,655
3 votes
Accepted

Nonharmonic solutions of Laplace's equation

Here's a counterexample in $n\ge3$ dimensions. With $\lVert\cdot\rVert$ denoting the Euclidean norm, set $$ f(x)=\begin{cases} x_1x_2x_3\lVert x\rVert^{-n-4},&{\rm if\ }x\not=0,\cr 0,&{\rm if\ }x=0. \ …
George Lowther's user avatar