| Abstract: |
| We consider a nonlinear Schrodinger-type equation with a nonlocal potential, of convolution type, called the generalized Hartree equation. In the focusing case we investigate global behavior of solutions and formation of stable singularities. In the inter-critical regime we first obtain a dichotomy for global vs finite time existing solutions exhibiting two methods of obtaining scattering: one via Kenig-Merle concentration - compactness and another one is using Dodson-Murphy approach. Next, we investigate stable blow-up regime in a critical case and describe the blow-up dynamics. |
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