{"title":"耦合均匀化和大偏差,及其在非局部抛物型偏微分方程中的应用","authors":"A. Coulibaly","doi":"10.22436/jnsa.016.03.03","DOIUrl":null,"url":null,"abstract":"Consider the following nonlocal integro-differential operator of L´evy-type L α ε , δ given by L αε , δ f ( x ) := (cid:90) R d \\{ 0 } (cid:20) f (cid:16) x + εσ (cid:16) x δ , y (cid:17)(cid:17) − f ( x ) − εσ i (cid:16) x δ , y (cid:17) ∂ i f ( x ) 1 B ( y ) (cid:21) ν αε ( dy ) + (cid:20)(cid:16) ε δ (cid:17) α − 1 b i 0 (cid:16) x δ (cid:17) + b i 1 (cid:16) x δ (cid:17)(cid:21) ∂ i f ( x ) , related to stochastic differential equations driven by multiplicative isotropic α -stable L´evy noise (1 < α < 2). We study by using homogenization theory the behavior of u ε , δ : R d −→ R of double perturbed Kolmogorov, Petrovskii and Piskunov (KPP)-type with periodic coefficients varying over length scale δ and nonlinear reaction term of scale 1 /ε , (cid:14)","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"102 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Coupling homogenization and large deviations, with applications to nonlocal parabolic partial differential equations\",\"authors\":\"A. Coulibaly\",\"doi\":\"10.22436/jnsa.016.03.03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider the following nonlocal integro-differential operator of L´evy-type L α ε , δ given by L αε , δ f ( x ) := (cid:90) R d \\\\{ 0 } (cid:20) f (cid:16) x + εσ (cid:16) x δ , y (cid:17)(cid:17) − f ( x ) − εσ i (cid:16) x δ , y (cid:17) ∂ i f ( x ) 1 B ( y ) (cid:21) ν αε ( dy ) + (cid:20)(cid:16) ε δ (cid:17) α − 1 b i 0 (cid:16) x δ (cid:17) + b i 1 (cid:16) x δ (cid:17)(cid:21) ∂ i f ( x ) , related to stochastic differential equations driven by multiplicative isotropic α -stable L´evy noise (1 < α < 2). We study by using homogenization theory the behavior of u ε , δ : R d −→ R of double perturbed Kolmogorov, Petrovskii and Piskunov (KPP)-type with periodic coefficients varying over length scale δ and nonlinear reaction term of scale 1 /ε , (cid:14)\",\"PeriodicalId\":22770,\"journal\":{\"name\":\"The Journal of Nonlinear Sciences and Applications\",\"volume\":\"102 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Nonlinear Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22436/jnsa.016.03.03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/jnsa.016.03.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Coupling homogenization and large deviations, with applications to nonlocal parabolic partial differential equations
Consider the following nonlocal integro-differential operator of L´evy-type L α ε , δ given by L αε , δ f ( x ) := (cid:90) R d \{ 0 } (cid:20) f (cid:16) x + εσ (cid:16) x δ , y (cid:17)(cid:17) − f ( x ) − εσ i (cid:16) x δ , y (cid:17) ∂ i f ( x ) 1 B ( y ) (cid:21) ν αε ( dy ) + (cid:20)(cid:16) ε δ (cid:17) α − 1 b i 0 (cid:16) x δ (cid:17) + b i 1 (cid:16) x δ (cid:17)(cid:21) ∂ i f ( x ) , related to stochastic differential equations driven by multiplicative isotropic α -stable L´evy noise (1 < α < 2). We study by using homogenization theory the behavior of u ε , δ : R d −→ R of double perturbed Kolmogorov, Petrovskii and Piskunov (KPP)-type with periodic coefficients varying over length scale δ and nonlinear reaction term of scale 1 /ε , (cid:14)