Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities
This paper studies time-periodic solutions of singularly perturbed Tikhonov systems of reaction–diffusion–advection equations with nonlinearities that include the square of the gradient of the unknown function (KPZ nonlinearities). The boundary layer asymptotics of solutions are constructed for Neum...
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| Veröffentlicht in: | Russian journal of mathematical physics 2024-09, Vol.31 (3), p.504-516 |
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| container_title | Russian journal of mathematical physics |
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| creator | Nikulin, E.I. Nefedov, N.N. Orlov, A.O. |
| description | This paper studies time-periodic solutions of singularly perturbed Tikhonov systems of reaction–diffusion–advection equations with nonlinearities that include the square of the gradient of the unknown function (KPZ nonlinearities). The boundary layer asymptotics of solutions are constructed for Neumann and Dirichlet boundary conditions. The study considers both the case of quasimonotone sources and systems without the quasimonotonicity condition. The asymptotic method of differential inequalities is used to prove theorems on the existence of solutions and their Lyapunov asymptotic stability.
DOI
10.1134/S1061920824030129 |
| doi_str_mv | 10.1134/S1061920824030129 |
| format | Article |
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DOI
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DOI
10.1134/S1061920824030129</description><subject>14/34</subject><subject>639/766/189</subject><subject>639/766/530</subject><subject>639/766/747</subject><subject>Advection</subject><subject>Advection-diffusion equation</subject><subject>Asymptotic methods</subject><subject>Boundary conditions</subject><subject>Boundary layer stability</subject><subject>Diffusion layers</subject><subject>Mathematical and Computational Physics</subject><subject>Nonlinearity</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Singular perturbation</subject><subject>Stability</subject><subject>Theoretical</subject><issn>1061-9208</issn><issn>1555-6638</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kU1OwzAQhSMEEqVwAHaWWAfG-XWWVfkVFVS0bNhETmJTl9QutlPIjjtwAq7GSXAIEgvEap7mvW9mpPG8QwzHGIfRyQxDgrMASBBBCDjItrwBjuPYT5KQbDvtbL_zd709Y5YACRCIBt7H2aswlsmSISorNDLtam2VFSWaWVqIWtgWKY5mqm6sUNIgrjSaMi1U5TJTqmmh6k5pVdRsZZCQaC6eFkqqjT9v1wzdMVp26Ofb-6ngvDG9HlUb9t1Hs9Yd4MgXYRfoevqAbpSshWRUCyuY2fd2OK0NO_ipQ-_-_Gw-vvQntxdX49HEL3FGrI-DJCpwlNKCJBmBisRAWRWxAFKIccShqgAXPCt5QWiakCQlYRxTICyjUVmm4dA76ueutXpumLH5UjVaupV5iHFAwjRNM5fCfarUyhjNeL7WYkV1m2PIu0_kfz7hmKBnjMvKR6Z_J_8PfQGyq49p</recordid><startdate>20240901</startdate><enddate>20240901</enddate><creator>Nikulin, E.I.</creator><creator>Nefedov, N.N.</creator><creator>Orlov, A.O.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240901</creationdate><title>Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities</title><author>Nikulin, E.I. ; Nefedov, N.N. ; Orlov, A.O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-1264b147ab86980d850aed4e2070514f0dd01bf9cfb8a768678355a08e9a4cc73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>14/34</topic><topic>639/766/189</topic><topic>639/766/530</topic><topic>639/766/747</topic><topic>Advection</topic><topic>Advection-diffusion equation</topic><topic>Asymptotic methods</topic><topic>Boundary conditions</topic><topic>Boundary layer stability</topic><topic>Diffusion layers</topic><topic>Mathematical and Computational Physics</topic><topic>Nonlinearity</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Singular perturbation</topic><topic>Stability</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nikulin, E.I.</creatorcontrib><creatorcontrib>Nefedov, N.N.</creatorcontrib><creatorcontrib>Orlov, A.O.</creatorcontrib><collection>CrossRef</collection><jtitle>Russian journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nikulin, E.I.</au><au>Nefedov, N.N.</au><au>Orlov, A.O.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities</atitle><jtitle>Russian journal of mathematical physics</jtitle><stitle>Russ. J. Math. Phys</stitle><date>2024-09-01</date><risdate>2024</risdate><volume>31</volume><issue>3</issue><spage>504</spage><epage>516</epage><pages>504-516</pages><issn>1061-9208</issn><eissn>1555-6638</eissn><abstract>This paper studies time-periodic solutions of singularly perturbed Tikhonov systems of reaction–diffusion–advection equations with nonlinearities that include the square of the gradient of the unknown function (KPZ nonlinearities). The boundary layer asymptotics of solutions are constructed for Neumann and Dirichlet boundary conditions. The study considers both the case of quasimonotone sources and systems without the quasimonotonicity condition. The asymptotic method of differential inequalities is used to prove theorems on the existence of solutions and their Lyapunov asymptotic stability.
DOI
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| source | Springer Journals |
| subjects | 14/34 639/766/189 639/766/530 639/766/747 Advection Advection-diffusion equation Asymptotic methods Boundary conditions Boundary layer stability Diffusion layers Mathematical and Computational Physics Nonlinearity Physics Physics and Astronomy Singular perturbation Stability Theoretical |
| title | Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities |
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