| Abstract: |
| In this talk, we construct localizing solutions for diffusion-relaxation systems by exploiting their
self-similar structure. Diffusion-relaxation models arise in a wide range of applications, from
shear-induced motion to biological chemotaxis, and exhibit equilibration and localization depending
on parameter regimes. We extend the self-similar formulation to multi-dimensional
domains and analyze the resulting asymptotic behavior of solutions. Using geometric singular
perturbation theory and the Poincar\'e-Bendixson lemma on a perturbed invariant manifold, we
establish the existence of localized self-similar solutions. |
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