An $L_q(L_p)$-theory for time-fractional diffusion equations with nonlocal operators generated by Lévy processes with low intensity of small jumps

Kang, Jae-Hoon; Park, Daehan

doi:10.48550/arxiv.2110.01800

Cited by 3 publications

(2 citation statements)

References 34 publications

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“…Particularly for γ < 2, these operators can be represented in a form of non-local operators. We refer to [9,14,18,24,26,27,28,37,38,39,40,49,50] for L p -theories with generators of stochastic processes and non-local operators. We also introduce papers [41,42,43] handling general operators with smooth symbols in L p -spaces based on a H ∞ -calculus approach.…”

Section: Introductionmentioning

confidence: 99%

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Ho¹

2023

Preprint

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Since the Seoul Metropolitan Area, Republic of Korea, is highly populated, a large number of people are frequently exposed to high concentrations of particulate matter (PM) with mean aerodynamic diameters of <= 10 mm (PM10) in cold season. The concentration of PM10 in Seoul Metropolitan Area increases by transboundary transport, local direct emissions, and chemical reactions of aerosol precursors in the atmosphere. Here, the Seoul Metropolitan Area (Seoul, Gyeonggi-do, and Incheon) and surrounding region (Chungcheongnam-do, Daejeon, and Sejong) are regionally classified by clustering analysis based on the variability of PM10 concentrations. According to the inertia score by the number of clusters, the optimum cluster number of regional variability of PM10 is four. The region of cluster 1 is divided into southern Gyeonggi-do and eastern Chungcheongnam-do, the cluster 2 is mainly classified Incheon, western Gyeonggi-do, and Seoul. The cluster 3 region is western Chungcheongnam-do adjacent to Yellow Sea, and the cluster 4 is classified into eastern Gyeonggi-do. The variability of PM10 in each region is distinguished by the local chemical pollutants emission and weather conditions such as wind speed and direction in each region. This regional classification of PM10 variability is different from administrative districts. Considering most of policies for responding to high concentrations of PM10 are being prepared by administrative districts, this study suggests that a response on the basis of these regional PM10 distribution would be more effective way to improve air quality in the Seoul Metropolitan and Chungcheong Area.

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Section: Introductionmentioning

confidence: 99%

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Ho¹

2023

Preprint

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“…However, these days beyond second-order operators, there occur numerous interesting researches handling high-order operators, nonlocal operators, and pseudo-differential operators (cf. [2,3,4,9,17,19,20,22,23,26,33,34,35,36,46,47]). Even for stochastic PDEs, there have been improvements in L p -theories for various operators (cf.…”

Section: Introductionmentioning

confidence: 99%

A weighted $L_p$-regularity theory for parabolic partial differential equations with time measurable pseudo-differential operators

Choi¹,

Kim²

2022

Preprint

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We obtain the existence, uniqueness, and regularity estimates of the following Cauchy problemin (Muckenhoupt) weighted Lp-spaces with time-measurable pseudo-differential operatorsMore precisely, we find sufficient conditions of the symbol ψ(t, ξ) (especially depending on the smoothness of the symbol with respect to ξ) to guarantee that equation (0.1) is well-posed in (Muckenhoupt) weighted Lp-spaces. Here the symbol ψ(t, ξ) is merely measurable with respect to t and the sufficient smoothness of ψ(t, ξ) with respect to ξ is characterized by a property of each weight. In particular, we prove the existence of a positive constant N such that for any solution u to equation (0.1),where p, q ∈ (1, ∞), −d − 1 < α < (d + 1)(p − 1), −1 < α1 < q − 1, −d < α2 < d(p − 1), and γ is the order of the operator ψ(t, i∇).

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On $$L_{p}-$$ Theory for Integro-Differential Operators with Spatially Dependent Coefficients

Janreung,

Siripraparat,

Saksurakan

2024

Potential Anal

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An $L_q(L_p)$-theory for time-fractional diffusion equations with nonlocal operators generated by Lévy processes with low intensity of small jumps

Cited by 3 publications

References 34 publications

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

A weighted $L_p$-regularity theory for parabolic partial differential equations with time measurable pseudo-differential operators

On $$L_{p}-$$ Theory for Integro-Differential Operators with Spatially Dependent Coefficients

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