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Blow-up versus global existence of solutions to aggregation equations

Grzegorz Karch, Kanako Suzuki (2011)

Applicationes Mathematicae

A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.

Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables

Maria Ewa Pliś, Bogdan Ziemian (1997)

Annales Polonici Mathematici

We consider a nonlinear Laplace equation Δu = f(x,u) in two variables. Following the methods of B. Braaksma [Br] and J. Ecalle used for some nonlinear ordinary differential equations we construct first a formal power series solution and then we prove the convergence of the series in the same class as the function f in x.

Borel summable solutions of the Burgers equation

Grzegorz Łysik (2009)

Annales Polonici Mathematici

We give necessary and sufficient conditions for the formal power series solutions to the initial value problem for the Burgers equation t u - x ² u = x ( u ² ) to be convergent or Borel summable.

Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations

Jakob Yngvason (2008/2009)

Séminaire Équations aux dérivées partielles

One of the most interesting phenomena exhibited by ultracold quantum gases is the appearance of vortices when the gas is put in rotation. The talk will bring a survey of some recent progress in understanding this phenomenon starting from the many-body ground state of a Bose gas with short range interactions. Mathematically this amounts to describing solutions of a linear Schrödinger equation with a very large number of variables in terms of a nonlinear equation with few variables and analyzing the...

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