ON GLOBAL EXISTENCE OF AN IMPLICIT FUNCTION

In this paper, we prove the existence and uniqueness of solutions for a nonlocal, fourth-order integro-differential equation that models electrostatic MEMS with parallel metallic plates by exploiting a well-known implicit function theorem on the topological space framework. As the diameter of the domain is fairly small (similar to the length of the device wafer, which is comparable to the distance between the plates), the fringing field phenomenon can arise. Therefore, based on the Pelesko–Driscoll theory, a term for the fringing field has been considered. The nonlocal model obtained admits solutions, making these devices attractive for industrial applications whose intended uses require reduced external voltages.

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Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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The Affective Politics of Karma among Buddhist Cancer Charities in Vietnam

Journal of Vietnamese Studies ◽

10.1525/vs.2020.15.4.33 ◽

2020 ◽

Vol 15 (4) ◽

pp. 33-62

Author(s):

Sara Swenson

Keyword(s):

Public Health ◽

Global Existence ◽

Food Production ◽

Public Health Intervention ◽

Health Intervention ◽

Moral Failure ◽

Cancer Rates ◽

Charity Work

In this article, I explore how Buddhist charity workers in Vietnam interpret rising cancer rates through understandings of karma. Rather than framing cancer as a primarily physical or medical phenomenon, volunteers state that cancer is a product of collective moral failure. Corruption in public food production is both caused by and perpetuates bad karma, which negatively impacts global existence. Conversely, charity work creates merit, which can improve collective karma and benefit all living beings. I argue that through such interpretations of karma, Buddhist volunteers understand their charity at cancer hospitals as an affective and ethical form of public health intervention.

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