Preprints - IAM Publications


	2021 Barbara Niethammer, Robert L. Pego, André Schlichting and Juan J. L. Velázquez Oscillations in a Becker-Döring model with injection and depletion 2021 https://ui.adsabs.harvard.edu/abs/2021arXiv210206751N

	2019 Jian-Guo Liu, B. Niethammer and Robert L. Pego Self-similar Spreading in a Merging-Splitting Model of Animal Group Size Journal of Statistical Physics: 102 2019 10.1007/s10955-019-02280-w

	Barbara Niethammer and Richard Schubert A local version of Einstein's formula for the effective viscosity of suspensions arXiv e-prints: arXiv:1903.08554 2019 https://ui.adsabs.harvard.edu/#abs/2019arXiv190308554N

	2018 M. Bonacini, B. Niethammer and JJL Velázquez Self-similar gelling solutions for the coagulation equation with diagonal kernel 2018 https://arxiv.org/abs/1711.02966

	M. Bonacini, B. Niethammer and JJL Velázquez Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity 2018 https://arxiv.org/abs/1612.06610

	B. Niethammer, A. Nota, S. Throm and J.J.L. Velázquez Self-similar asymptotic behavior for the solutions of a linear coagulation equation 2018 https://arxiv.org/abs/1804.08886

	B. Niethammer and J. J. L. Velázquez Oscillatory traveling wave solutions for coagulation equations Quart. Appl. Math., 76(1): 153--188 2018 10.1090/qam/1478

	2017 Marco Bonacini, B. Niethammer and J.J. L. Velázquez Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity smaller than one 2017 https://arxiv.org/abs/1704.08905

	Marco Bonacini, B. Niethammer and J.J. L. Velázquez Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity one 2017 https://arxiv.org/abs/1612.06610

	2016 Michael Herrmann, Barbara Niethammer and Juan J. L. Velázquez Instabilities and oscillations in coagulation equations with kernels of homogeneity one 2016 http://arxiv.org/abs/1606.09405

	P. Laurençot, B. Niethammer and J. J. L. Velázquez Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel 2016 http://arxiv.org/abs/1603.02929

	2015 Barbara Niethammer, Sebastian Throm and Juan J. L. Velázquez A revised proof of uniqueness of self-similar profiles to Smoluchowski's coagulation equation for kernels close to constant 2015 http://arxiv.org/abs/1510.03361

	Barbara Niethammer, Juan J. L. Velázquez and Michael Helmers Mathematical analysis of a coarsening model with local interactions 2015 http://arxiv.org/abs/1509.04917

	Barbara Niethammer, Sebastian Throm and Juan J. L. Velázquez Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels Ann. I. H. Poincaré - AN 2015 http://dx.doi.org/10.1016/j.anihpc.2015.04.002

	2014 Barbara Niethammer and Juan J. L. Velázquez Exponential tail behaviour of self-similar solutions to Smoluchowski's coagulation equation Communications in Partial Differential Equations, 39(12): 2314-2350 2014 http://dx.doi.org/10.1080/03605302.2014.918143 Abstract: We consider self-similar solutions with finite mass to Smoluchowski's coagulation equation for rate kernels that have homogeneity zero but are possibly singular such as Smoluchowski's original kernel. We prove pointwise exponential decay of these solutions under rather mild assumptions on the kernel. If the support of the kernel is sufficiently large around the diagonal we also proof that \( \lim_{x\rightarrow\infty}\frac{1}{x}\log\left(\frac{1}{f(x)}\right)\) exists. In addition we prove properties of the prefactor if the kernel is uniformly bounded below.

	Barbara Niethammer and Juan J. L. Velázquez Uniqueness of self-similar solutions to Smoluchowski's coagulation equations for kernels that are close to constant J. Stat. Phys., 157(1): 158-181 2014 http://dx.doi.org/10.1007/s10955-014-1070-3 Abstract: We consider self-similar solutions to Smoluchowski's coagulation equation for kernels K=K(x,y) that are homogeneous of degree zero and close to constant in the sense that \[ -\varepsilon \leq K(x,y)-2 \leq \varepsilon \Big(\Big(\frac{x}{y}\Big)^{\alpha} + \Big(\frac{y}{x}\Big)^{\alpha}\Big) \] for \(\alpha \in [0,1)\). We prove that self-similar solutions with given mass are unique if \(\varepsilon\) is sufficiently small which is the first such uniqueness result for kernels that are not solvable. Our proof relies on a contraction argument in a norm that measures the distance of solutions with respect to the weak topology of measures.

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