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3
votes
1answer
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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
123 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
162 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?
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