Questions about partial differential equations of parabolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

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6
votes
1answer
947 views

Short time existence on nonlinear parabolic PDE

I saw several papers that without proof accept the fact "Short time existence on nonlinear parabolic PDE" is there any affirmative proof of this fact? in which book we have this fact, the number of ...
2
votes
1answer
349 views

A comparison principle for parabolic equation

(Crossposted from http://math.stackexchange.com/questions/757672/how-to-prove-comparison-principle-for-parabolic-pde-nonlinear) Suppose $F:\mathbb{R} \to \mathbb{R}$ is smooth with $F(x) > 0$ for ...
5
votes
3answers
325 views

Structure of sign changes under the heat flow

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, ...
0
votes
0answers
102 views

Solving a parabolic PDE with boundary conditions given over ranges

How can one solve a Parabolic PDE (like the wave or diffusion equations) if the boundary conditions were given over ranges? Here is an example: How to solve the equation ...