### A one-dimensional spot welding model.

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We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter ${u}_{*}$ does not exceed a critical value ${u}_{*}^{c}$. The latter is the limit of a decreasing sequence $\left({u}_{*}^{k}\right)$ of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...