Abstract
AbstractThis work’s major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under a smallness assumption on the intial data. As an application, we provide a new well-posedness theory for a diffusion-dominant cross-diffusion system that originates from a hopping model with size exclusions. Our approach is based on a fixed point argument in a function space that is induced by suitable Carleson-type measures.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
Reference37 articles.
1. H. Amann. Dynamic theory of quasilinear parabolic systems. III. Global existence. Math. Z., 202(2):219–250, 1989.
2. S. B. Angenent. Nonlinear analytic semiflows. Proc. Roy. Soc. Edinburgh Sect. A, 115(1-2):91–107, 1990.
3. S. B. Angenent. Parabolic equations for curves on surfaces. I. Curves with $$p$$-integrable curvature. Ann. of Math. (2), 132(3):451–483, 1990.
4. J. Berendsen, M. Burger, V. Ehrlacher, and J.-F. Pietschmann. Uniqueness of strong solutions and weak–strong stability in a system of cross-diffusion equations. J. Evol. Equ., 20(2):459–483, 2020.
5. B. Bozzini, D. Lacitignola, C. Mele, and I. Sgura. Coupling of morphology and chemistry leads to morphogenesis in electrochemical metal growth: a review of the reaction-diffusion approach. Acta Appl. Math., 122:53–68, 2012.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献