# Questions tagged [differential-equations]

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

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### Non constant delay differential equations

Given $\varphi:[0,1] \to [0,1]$ a continuous function, let $(E)$ be the delay differential equation (I am not sure about the terminology, as the delay is non constant): $y'(t) = y(\varphi(t))$. It is ...
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### What is Bouziani space and what are its applications in mathematics?

I have accrossed a new topological space seems were derived from Hilbert Space and it used to solve some boundary value problem for PDE and ODE , Inspired by this paper (page 4, Definition 3.1) , The ...
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### Discretization formula for system of two differential equations. “Solution to one of these is the initial condition of the other”. In which sense?

Consider the following stochastic differential equation \begin{equation} dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1} \end{equation} where $A$, $B$ and $C$ are parameters ...
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### Is this curve well known?

I consider the curve $c(t)=(x(t),y(t))$ in $\mathbb{R}^2$ such that $\frac{d^2x(t)}{dt^2}=-(a\sin t+b)\frac{dy(t)}{dt}$ $\frac{d^2y(t)}{dt^2}=(a\sin t+b)\frac{dx(t)}{dt}$ $a,b\in\mathbb{R}$ Is the ...
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### Is there a standard definition of weak form of a nonlinear PDE?

Comments on the question Are those distributional solutions that are functions, the same as weak solutions? suggest there might not be a standard definition of the weak form of a non-linear PDE. Is ...
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### Are those distributional solutions that are functions, the same as weak solutions?

There are two closely related concepts and I am not sure exactly how close. Consider a partial differential equation. (The coefficients need not be constant but assume they are functions, and not ...
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### $x '(t) + g (x (t)) = f (t),\quad \forall t\in \mathbb R$ have periodic solution $\iff\; \frac 1T \int_0 ^ T f (t) dt \in g (\mathbb R)$

I have a research work concerning the equation: $$x '(t) + g (x (t)) = f (t),\quad \forall t\in \mathbb R$$ f and g are defined and continuous in $\mathbb R$ and with values ​​in $\mathbb R$. ...
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### What is an “exact solution” to a PDE?

Wolfram MathWorld says As used in physics, the term “exact” generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...
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### BSDE without volatility

Let $(W_t)_{0\leq t\leq 1}$ be a standard Wiener process on $[0,1]$, and let $\mathcal{F}_t$ be the natural filtration. Consider a BSDE $$dX_t=f(t,X_t)dt+\sigma(t,X_t) dW_t$$ with terminal condition ...