Questions tagged [integral-equations]

This tag is about questions regarding the integral equations. An integral equation is an equation in which the unknown function appears under the integral sign. There is no universal method for solving integral equations. Solution methods and even the existence of a solution depend on the particular form of the integral equation.

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Convolution equation equals a constant

How would you solve this? I did the standard way of solving questions like these - I took the Laplace of both sides and used the convolution identity. But the solution I got, $f(t)=3+t^2/2$, does not ...
1 vote
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Crystallization Process Integral Equation with Arrhenius Functions

I am working on a mathematical model describing the crystallization process, represented by an integral equation involving the crystalline fraction $\xi_V(T, t)$, where $T$ is the temperature and $t$ ...
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How do I solve this differential-integral equation? [closed]

The following equation has come up in my research and I am lost at where to start. I have tried guessing forms of the solution and Mathematica is not helpful. Any help pointing me in the right ...
1 vote
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ring meniscus at cylinder

I came across a somewhat interesting differential equation while studying the shape of a meniscus ring formed at the bottom of a cylinder. Here are some 2D cross sections through a cylinder symmetry ...
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Lower bound of a trigonometric integral

Let $\alpha$, $\beta$, and $\gamma$ be non-zero real numbers. Further, suppose that $f$ and $g$ are probability density functions defined on $\mathbb{R}$. I'm interested in computing a lower bound of ...
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What are the conditions for solution of nonlinear Fredholm equations with Banach fixed point theorem?

Consider the nonlinear Fredholm integral equation of the second kind: $$\varphi(x) = f(x) + \lambda \int_a^b F(x, t, \varphi(t)) \, dt$$ where $(f)$ and $(K)$ are given functions, $(a, b)$ are ...
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Non-local boundary condition and integral equations

I'm solving initial value problem with non-local boundary condition $u(0,t)=\int_{0}^{l}\beta(s)u(s,t)ds = \gamma(t)$. I have already found function u for to cases $x<t$ and $x>t$. But I have ...
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Continuous dependence on initial conditions of Fredholm integral equation of the second kind

In several papers and other sources, I have seen statements about it being `well-known' that the Fredholm integral equation of the second kind is well-posed, in contrast to a Fredholm integral ...
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