I want to find a function (or a set of functions) such that $u(x,t)$ satisfies the following partial integro-differential equation with singular kernel \begin{eqnarray} &&u_x(0,t) = \int_0^t \frac{u_\lambda(0,\lambda)}{\sqrt{t-\lambda}} d\lambda, \\ &&u(0,0) = 0. \end{eqnarray} I tried the Laplace transform method but i couldn't find the solution.
Some help would be greatly appreciated.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.