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We study a two dimensional collision problem for a rigid solid immersed in acavity filled with a perfect fluid. We are led to investigate the asymptoticbehavior of the Dirichlet energy associated to the solution of a LaplaceNeumann problem as the distance $\varepsilon>0$ between the solid and thecavity's bottom tends to zero. Denoting by $\alpha>0$ the tangency exponent atthe contact point, we prove that the solid always reaches the cavity in finitetime, but with a non zero velocity for $\alpha <2$ (real shock case), and withnull velocity for $\alpha \geqslant 2$ (smooth landing case). Our proof isbased on a suitable change of variables sending to infinity the cuspsingularity at the contact. More precisely, for every $\varepsilon\geqslant 0$,we transform the Laplace Neumann problem into a generalized Neumann problem seton a domain containing a horizontal strip $]0,\ell_\varepsilon[\times ]0,1[$,where $\ell_\varepsilon\to +\infty$.

Asymptotic analysis of a Neumann problem in a domain with cusp. Application to the collision problem of rigid bodies in a perfect fluid