1
vote
0answers
24 views

existence and uniqueness of volterra integral equation of the first kind

$$ \int_0^t k(s,t)f(s)ds=g(t) $$ To know the existence and uniquness of solution of volterra integral equation(VIE) of the first kind, we differentiate it and convert to the VIE of the second kind. ...
0
votes
0answers
25 views

Solving an integral equation in general

I have an integral equation such that $$\int_t^Tf(s)g(s,t)~ds=h(t)$$ where $g$ and $h$ is given. we want to know function $f$ explicitly. As I know, this type of question is about the integral ...
25
votes
2answers
2k views

Why are mathematician so interested to find theory for solving partial differential equations but not for integral equation?

Why are mathematician so interested to find theory for solving partial differential equations (for example Navier-Stokes equation) but not for integral equations?
0
votes
0answers
66 views

Series solution for coupled PDEs

So I have this system for $f(z, v, t)$ and $\Psi(z, t)$, $$ \frac{\partial f}{\partial t} + v \frac{\partial f}{\partial z} - g(v) \frac{\partial \Psi}{\partial z} = 0 \tag{1} $$ $$ \frac{\partial^2 ...
2
votes
0answers
52 views

reference request: a graduate level textbook on viscosity solutions of IPDEs

I am particularly interested in IPDE which arises from optimal stopping/control problems so I would like some references on integral-partial differential equations, which are related this area. I have ...
3
votes
1answer
2k views

How to solve partial integro-differential equation?

Suppose the following partial integro-differential equation for a function $u(x,t)$ with $t\geq0$, $x \in [0,L]$: $\partial_t u = \partial_{xx} u + f(u,\lambda)$ $\lambda = B\left(u_0 - \int_{x=0}^L ...
0
votes
0answers
297 views

Relationship between integral equations and partial differential equations

In my functional analysis class, we did a lot of problems involving integral equations such as proving existence & uniqueness using spectral theory and the Banach fixed point theorem. I've never ...
1
vote
1answer
276 views

Partial integro-differential equation

I don't know if there is a method to solve this following integro - differential equation: $$\partial_t{u(x,t)}\int_{0}^{x}u(\zeta,t)d\zeta=\partial_{xx}u(x,t)$$ Can someone give me some hint? ...