# Tagged Questions

Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.

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### I need to know the most active research topic which depend on Real analysis and functional analysis? [on hold]

I need to know the most current topic in pure math with depend mainly on real analysis and functional analysis and not need a good knowledge in algebra and geomtry ? is delay differntial equations is ...
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### An innocuous second order linear ODE [on hold]

Is there much work done on equations of the form $$y'' + \alpha(t)y = 0,$$ where $\alpha(t) \in C^\infty([0,\infty))$ and $\alpha(t) > 0$? In particular, I am looking for some blow-up results. I ...
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### I can't derive the integrating factor of this first order linear Equation [on hold]

I can't derive the integrating factor of this first order linear Equation (x2 - y2 - y) dx - (x2 - y2 - x) dy = O. the answer is: integrating factor = 1/(x2 - y2)
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### Symbol of differential operator and change of variables [closed]

Recently I posted the following question on stack exchange, but it remained with no answer http://math.stackexchange.com/questions/1863658/symbol-of-differential-operator-and-change-of-coordinates I ...
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### Questions about the regularity of the solution of the heat equation in a bounded domain [closed]

I have questions about the proof of the following theorem: Theorem 8 (Smoothness). Suppose $u\in C^2_1(U_T)$ solves the heat equation in $U_T$. Then $u\in C^\infty(U_T)$ Here is the statement and ...
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### How do spectrums interact with bi-Lipschitz maps?

If it makes things simple, we can just stick to bi-Lipschitz maps from $S^k \rightarrow \mathbb{R}^d$ (w.r.t geodesic distance on the sphere with the standard round metric and the $2-$norm on the ...
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### When is a limit cycle generated by a Hamiltonian oval stable?

Consider a real polynomial $H$ of degree $n+1$ in the plane. A closed, connected component of a level curve $H=t$ is denoted by $\gamma(t)$ and called an oval of $H$. Let $\omega$ be a real 1-form ...
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### 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 ...
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### Dynamics of pairwise distances in the $n$-body problem

Disclaimer: I have asked this question on Physics SE a week ago, but got no answers. I know that some MO users are interested in the $n$-body problem, so I decided to cross post here as well. ...
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### Connection between cardiac equations and untangling knots?

I was surprised to learn that there is (conjecturally) a connection between a cardiac muscle model known as the FitzHugh-Nagumo equations, and untangling knots: Maucher, Fabian, and Paul Sutcliffe....
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### Injectivity/Surjectivity of $F_A :=\frac{d}{dt} +A(t)$ for a hyperbolic path of matrices $A(t)$ on $H^1$

I am looking for a reference to the following problem: Given a hyperbolic (no purely imaginary eigenvalues), continuous path of matrices $A(t)$ in $\mathbb{R}$ with hyperolic limits at $\pm \infty$. ...
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### How to learn concepts of Functional Analysis which are common in PDE

I am a master student and working in PDE area. I am trying to gain deep understanding of some of the concepts in functional analysis which are common tools in PDE research, such as weak*-topology, ...
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### Analytic conjugacy of vanishing holonomy groups implies analytic conjugacy of foliations

i am reading and trying to do some exercises and problems of the book Lectures on Analytic Differential Equations- Y. Ilyashenko, S. Yakovenko. I can not solve the problem 11.6 that says Consider ...
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### PDE with harmonic function [closed]

I'm looking for the solution of the following equation $$2cE^3=E_u^2+ E_v^2$$ where $c$ is a constant and $E$ is an harmonic function w.r. to the variables $u$ and $v$.
I have the following differential equation: $$V(z) = e^z [1-\varphi(\gamma)]+(\gamma-g)V'(z)+\frac{1}{2}\kappa^2 V''(z)$$ with $$e^z \varphi'(\gamma) = V'(z)$$ where $\varphi(\cdot)$ is a ...