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Results tagged with differential-equations
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user 27404
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
3
votes
Accepted
Uniqueness for a non-local differential equation
The answer is yes: f=g. I wrote up a paper with a more general result here. The idea is the following. If $f$ were assumed to be of Laplace transform type
$$
f(t,x) = \frac{1}{x} \int_0^\infty e^{ …
- 468
7
votes
1
answer
553
views
Uniqueness for a non-local differential equation
Question:Fix $\epsilon>0$. Consider the differential equation, defined for functions $f(t,x)\in C^\infty([0,\epsilon]\times[0,\epsilon])$ defined by
$$\frac{\partial}{\partial t} f(t,x)=\frac{f(t,x)^ …
- 468
1
vote
Hörmander's hypoellipticity theorem for complex coefficients
As Bazin notes, the situation is more complicated for complex vector fields.
For example, Kohn (Annals of Mathematics, 162 (2005), 943–986) gave an example of an $L^2$ sum of squares of complex vector …
- 468