Variational methods for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening

Fuchs, Martin; Serëgin, G.

doi:10.1002/(sici)1099-1476(19990310)22:4<317::aid-mma43>3.0.co;2-a

Math. Meth. Appl. Sci.

1999

DOI: 10.1002/(sici)1099-1476(19990310)22:4<317::aid-mma43>3.0.co;2-a

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Variational methods for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening

Martin Fuchs

¹

,

G. Serëgin

²

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Cited by 44 publications

(25 citation statements)

References 19 publications

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“…Up to now the regularity theory for weak solutions u P W 1 G W of (1.1) is very poor. Roughly speaking, in the papers [5], [6], [4] and [3] we demonstrated C 1 -regularity in case n 2, whereas for n^3 some partial C 1 -results were established. But again G is required to be of class C 2 together with some extra coercivity conditions.…”

Section: Now We Can State Our Main Resultmentioning

confidence: 80%

$L^{\infty }$-bounds for elliptic equations on Orlicz-Sobolev spaces

Fuchs

¹

,

Li

²

1999

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…Up to now the regularity theory for weak solutions u P W 1 G W of (1.1) is very poor. Roughly speaking, in the papers [5], [6], [4] and [3] we demonstrated C 1 -regularity in case n 2, whereas for n^3 some partial C 1 -results were established. But again G is required to be of class C 2 together with some extra coercivity conditions.…”

Section: Now We Can State Our Main Resultmentioning

confidence: 80%

$L^{\infty }$-bounds for elliptic equations on Orlicz-Sobolev spaces

Fuchs

¹

,

Li

²

1999

Self Cite

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…We here use a technique due to Frehse and Seregin (see [FrS]) which has also been applied in [FO], [FS2], [FR] and [BF4]. From now on assume that we are in the situation of Theorem 2.1, b).…”

Section: Let Us Recallmentioning

confidence: 81%

Variants of the Stokes Problem: the Case of Anisotropic Potentials

Bildhauer

¹

,

Fuchs

²

2003

Journal of Mathematical Fluid Mechanics

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…where c 1 , c 2 are positive constants, and s, p are defined by (23); assume further that M can be written as the a.…”

Section: Semismooth Functionsmentioning

confidence: 99%

“…Thankfully, at this point we can make use of regularity results that guarantee the boundedness of gradients for Bingham and Herschel-Bulkley models [23,24]. Noting also that the mapping D D D(u ε ) → S S S ε defined by the relation ( 6) is Lipschitz continuous [30,Lm.…”

Section: The Bingham Constitutive Relationmentioning

confidence: 99%

A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow

Gazca‐Orozco

¹

2021

Get access via publisher Add to collection Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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