Ordinary-or partial differential equations. Delay differential equations, neutral equations, integrodifferential equations. Well-posedness, asymptotic behavior and related questions.
0
votes
0answers
49 views
weak form in Hamilton Jacobi PDE and to include an Dirichlet bound conditions
I tried to solve the next PDE with finite elements, therefore I need to make a weak form for:
$$\frac{\partial u}{\partial t}+\nu(\vec{x},t) \|\nabla u\| = 0$$ and to integrate the Dirichlet ...
-1
votes
1answer
55 views
Proving convergence of an integral-differential equation [closed]
I have a second order nonlinear ordinary differential equation which I transformed into an integral-differential equation by multiplying the ODE by $y'$ and integrating.
My question is where can I ...
2
votes
0answers
77 views
A natural tower of bundles over Grassmannian manifolds
There is a well-known exact sequence of vector bundles
$$
0\to U\to T\to N\to 0
$$
over a Grassmannian manifold $Gr(V,n)$: the fibers over $L\in Gr(V,n)$ are, respectively, $L$ itself, the whole $V$ ...
2
votes
1answer
83 views
Non-linear 1st order difference equation
I have been trying to solve the following difference equation for some time now : $$u^3(n+1) = a - b\cdot u^2(n) + u^3(n), \qquad a \ne 0 \ne b$$
I have tried various substitutions, simplifications ...
0
votes
0answers
59 views
Picard-Fuchs equation of elliptic curves with level $N$ structure.
Let $X_N$ be the moduli space of elliptic curves with level $N$ structure. Is the Piard Fuchs equation of the universal family over $X_N$ (take some covering if $X_N$ is not a fine moduli space)?
In ...
1
vote
0answers
18 views
requiring reference on the error bounds for the asymptotic expansions of an ODE of order greater than two
Let \begin{equation}
\sum_{j = 0}^{n} a_{ j}(z) w^{(j)} = 0
\end{equation}
be an ODE of order $n$, with $a_n(z) = 1$, $a_j(z) = a_{j, 0} + a_{j, 1} z^{-1} + ...$ holomorphic at $\infty$. It has a ...
0
votes
0answers
19 views
Existence of solution to 2nd-order linear ODE with a free boundary
Fix positive constants $L$, $R$, $\gamma$, $\mu$ and $\lambda$, with $\gamma>1$, $\lambda\in (0,1)$.
Is there a constant $W^1 > R$ and a function $b$ such that, for $w\in [R,W^1]$,
$$b(w) = ...
0
votes
0answers
33 views
Close to giving up on this differential equation! Please help! [migrated]
first of all I'm not a mathematician, so I apologize if any of my understanding and terminology isn't up to par. Also, I've never used this website (or any of these kind of question/answer) websites ...
2
votes
0answers
49 views
How to find solutions of non-linear ODE with particular BCs
What are some methods, numerical or otherwise, of finding solutions to nonlinear ODEs that satisfy particular boundary conditions? In particular, I'm looking for curves y(s) constrained to a ...
2
votes
0answers
90 views
Differential Equations vs Difference Equations
My question is:
Is there a duality between a solution of an ODE,PDE,SDE or integral equations with their analog counterpart in the discrete domain?
I mean if I know a solution to the difference ...
0
votes
1answer
104 views
The solvability of a Hölder ODE [closed]
The problem is follow, I want to know weather there is a function $u\in \text{C}^{0}\left((-1,1)\right)$ but not $\text{C}^1((-1,1))$, such that $\lim\limits_{h\rightarrow ...
2
votes
0answers
33 views
Rotation number of perturbated equation
I have a differential equation on torus $(t,x)$ and well studied it's Arnold tongues for Poincare map of the circle $x(t=0) \to x(t=2\pi)$. The question is how changes rotation number when I add small ...
2
votes
1answer
159 views
Geodesics and harmonic map heat flow
I believe the answer to my question is well-known, but as I do not know too much about harmonic map flows, here it goes:
Let $M$ be a complete Riemannian manifold. For a curves $c: [0,1] ...
1
vote
1answer
193 views
Best approach to solve this PDE
I need to solve this Partial Differential Equation for $\lambda(x,y)$,
$$\frac{\partial \lambda}{\partial x} + h(x,y)\frac{\partial \lambda}{\partial y} - \lambda \frac{\partial h}{\partial y} = 0$$ ...
3
votes
0answers
60 views
Classical parabolic theory (PDEs)
I am reading an articule(http://link.springer.com/content/pdf/10.1007%2Fs00028-010-0085-8.pdf) so I almost done but I dont understand the next argument is in the page 8 "It is known from the ...
