All Questions
Tagged with differential-calculus differential-equations
12 questions
58
votes
22
answers
12k
views
Which high-degree derivatives play an essential role?
Q. Which high-degree derivatives play an essential role
in applications, or in theorems?
Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration),
and the ...
3
votes
1
answer
268
views
An answer to this system of PDE's
Planning of the question:
Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle
The isotropic almost complex structures $J_{\delta , \sigma}$ were introduced by Aguilar on the ...
- 601
3
votes
1
answer
95
views
Inductive proof that $\dot{M}_{n+1}=-M_{n+1}+W^{(n+2)}(0)+vM_{n+2}$
The motivation for the following is to convert the integro-differential equation
\begin{equation}
\kappa\ddot x+\dot x=-kx+\beta\int_{-\infty}^t W'(x(t)-x(s))e^{s-t}ds,
\end{equation}
into a ...
- 79
2
votes
0
answers
182
views
Solve 4th order ODE with variable coefficients
I am trying to solve a 4th order boundary value problem with variable coefficients, namely the problem of a rotating cantilever beam:
$u'''' - \frac{((1-x^2)u')'}{2\eta} - \frac{\alpha}{\eta}((1-x)u')...
- 21
1
vote
1
answer
287
views
Approximate largest eigenvalue of Monodromy matrix
Does anyone know the procedure (or have pseudo code) to approximating the largest eigenvalue of a monodromy matrix? Or even to approximate the monodromy matrix itself?
There is no explicit solution ...
- 11
1
vote
0
answers
44
views
Differential system of equations I would like to simplify
I have 2 functions of time $f(t),g(t)$ and a condition for the time-derivative of a third function $h(t)$, say $$\dot{h}(t)=\dot{g}(t)\cos{f(t)},$$ so $h$ is defined provided a value for $h(0)$ (as $h(...
- 11
1
vote
0
answers
50
views
type of solutions of $-u^{\prime\prime}=\lambda e^{u}$ based on the value of the parameter $\lambda$. (Gelfand problem)
My question comes from the book
Stable solutions of elliptic partial differential equations, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics 143. Boca Raton, FL: CRC ...
- 11
1
vote
0
answers
103
views
Reference for numerical solutions for differential equations like $f'(x)=f(x+1)+f(x-1)$
One can solve a delay differential equation (like for example $f'(x)=f(x-1)$) if we have a function as a bounded condition (in my example we need to know $f$ on $[0,1)$) and then use a simple forward ...
- 121
0
votes
1
answer
162
views
Solutions of this system of PDE's
This question is related to the existence of Einstein metrics on tangent bundles where the metric is induced by the isotropic almost complex structures on the tangent bundle. I'm trying this on the ...
- 601
0
votes
1
answer
167
views
Solution of this differential equation [closed]
I wonder if it is possible to solve analytically the following equation
$$
\dot{\alpha}_t = -\frac{2}{m} \alpha^2_t + \frac{1}{2m} (\alpha_t - \alpha_t^*)^2
$$
Where $\alpha_t$ is a complex function, $...
0
votes
0
answers
29
views
On constructing the canonical boundary operator for a given differential operator
Given an $n\times n$ matrix $$X=\begin{pmatrix}
x_{11} & x_{12} & \cdots & x_{1n} \\
x_{21} & x_{22} & \cdots & x_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
x_{n1}...
- 765
-1
votes
1
answer
127
views
Solving a fully nonlinear first order PDE
given a symmetric matrix of Holder continuous functions $A(x)$ such that
$$
\frac{1}{C} |\xi|^2 \leq \langle A(x)\xi,\xi \rangle \leq C |\xi|^2
$$
find a vector field $\Phi$ such that
$$
D \Phi(x)^t D ...
- 261