Localization in Stationary Non-equilibrium Solutions for Multicomponent Coagulation Systems
We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a universal localization property. More precisely, we show th...
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| Veröffentlicht in: | Communications in mathematical physics 2021-11, Vol.388 (1), p.479-506 |
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| creator | Ferreira, Marina A. Lukkarinen, Jani Nota, Alessia Velázquez, Juan J. L. |
| description | We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a universal localization property. More precisely, we show that these solutions asymptotically localize into a direction determined by the source or by a flux constraint: the ratio between monomers of a given type to the total number of monomers in the cluster becomes ever closer to a predetermined ratio as the cluster size is increased. The assumptions on the coagulation kernel are quite general, with isotropic power law bounds. The proof relies on a particular measure concentration estimate and on the control of asymptotic scaling of the solutions which is allowed by previously derived estimates on the mass current observable of the system. |
| doi_str_mv | 10.1007/s00220-021-04201-z |
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The proof relies on a particular measure concentration estimate and on the control of asymptotic scaling of the solutions which is allowed by previously derived estimates on the mass current observable of the system.</description><subject>Asymptotic methods</subject><subject>Asymptotic properties</subject><subject>Classical and Quantum Gravitation</subject><subject>Clusters</subject><subject>Coagulation</subject><subject>Complex Systems</subject><subject>Equilibrium</subject><subject>Equilibrium conditions</subject><subject>Localization</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Monomers</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kDFPwzAQhS0EEqXwB5giMRvOduIkI6qAIhUYChOD5bh25SqxW9sZ2l9P2iCxMd1J9947vQ-hWwL3BKB8iACUAgZKMOQUCD6coQnJGcVQE36OJgAEMOOEX6KrGDcAUFPOJ-h74ZVs7UEm611mXbZMp1WGffbuHda73ra2CbbvsqVv--MtZsaH7K1vk1W-23qnXcpmXq77doxZ7mPSXbxGF0a2Ud_8zin6en76nM3x4uPldfa4wIpxlrBhVGvSKMOZUgQ4qXjTcKhovqpkyYqK8mLV5HWZs9rUWhumyhVjWpqSDB0aNkV3Y-42-F2vYxIb3wc3vBS0qFhecl7Ug4qOKhV8jEEbsQ22G3oKAuIIUYwQxQBRnCCKw2BioykOYrfW4S_6H9cPpQd21g</recordid><startdate>20211101</startdate><enddate>20211101</enddate><creator>Ferreira, Marina A.</creator><creator>Lukkarinen, Jani</creator><creator>Nota, Alessia</creator><creator>Velázquez, Juan J. 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| subjects | Asymptotic methods Asymptotic properties Classical and Quantum Gravitation Clusters Coagulation Complex Systems Equilibrium Equilibrium conditions Localization Mathematical and Computational Physics Mathematical Physics Monomers Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical |
| title | Localization in Stationary Non-equilibrium Solutions for Multicomponent Coagulation Systems |
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