English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This equation can be thought of as describing steady-state temperature distribution U{x) in a (one-dimensional, in our case) conducting medium in which a local voltage drop V(x) is mantained; a steady current makes each point into a heat source. The electrical resistivity at x is o(x)(U(x))r, where V2(x)/a(x) = K(x), and thermal conductivity is conventionally set to be one. This is a particular case of a problem treated in [1] for the transient case, [2, 3], and [4]. Equation (1) is subject to the usual boundary conditions. Analogies between one-dimensional diffusion and boundary layer problems in fluid dynamics are well known. In Sec. 4 we show how this electrical analogy can be used in the analysis of diffusion problems. In Sec. 2 we set up the two problems with the various boundary conditions we shall consider. In Sec. 3 we discuss the bibliography on the two problems, and the hypotheses made on the function K(x) in (1), related to the diffusivity in the diffusion context. In Sec. 4 we give, in I, a unified uniqueness proof for problems (2), (2.1)—(2.3) below; we give, in II and III, estimates for the values «(0) in (2.2) and tj, in (2.3), and in IV, we include an existence proof for (1) with boundary conditions t/(0) = 0, LU'(V) = t/(l) (cf. (4), (4.3)).

An equation with a singular nonlinearity related to diffusion problems in one dimension