# Questions tagged [delay-differential-equations]

98 questions
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### Using delay block in Simulink to account for flow rate in a fluid loop

I am trying to model a fairly simple cooling system loop where coolant flows over a battery to remove heat, then flows into a large reservoir where the coolant is mixed, coolant then flows out of the ...
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### Approximating $\max \big\{\frac{x_\tau}{x}\big\}$ as $x$ and $x_\tau \rightarrow 0^+$

I have the following delay system: $$x'(t) = g(t,\tau,x,x_\tau)$$ Given that $g(\cdot)$ is smooth and bounded, $x(t)$ is bounded in a non-negative region. What are some possible ways to obtain an ...
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### delay partial differential equations

In an effort to solve a delay partial differential equation $$\partial_t f(t,x)= \Phi(x) f(t,x)+\Psi(x) f(t,x-\alpha),$$ with $$f(0,x)=1,\hspace{0.3cm} f(t,0)=1$$ Where $\alpha$ is the delay ( a real ...
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### Prove that the solution to a delayed differential equation is positive for all $t>0$.

Prove that for the IVP \begin{cases} x'(t)=cx(t)[1-x(t-r)] \\ x(\mu)=\phi(\mu) & \mu \in [-r,0] \end{cases} for every $\phi\in C([-r,0],\mathbb{R})$ with $\phi(0)>0$, has a unique solution ...
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### All the solutions of $f'(x)=f(x+\pi/2)$

Consider the following equation (with $f \in C^{\infty}(\mathbb{R})$): $$f'(x)=f(x+\pi/2)$$ This equation is satisfied by $f(x) = A\cos(x) +B\sin(x)$, for any $A,B \in \mathbb{R}$. Question: What ...