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

New results on the existence, uniqueness and maximal regularity of a solution are given for a parabolic equation set in a non-regular domainQ  =    (  t  ,   x  1   )   ∈   ℝ  2   :  0  &lt;  t  &lt;  T  ;ϕ  1    (  t  )   &lt;   x  1   &lt;   ϕ  2    (  t  )    ×   ∏   i  =  1    N  -  1]  0  ,    b  i    [$ Q=\bigl \lbrace  (t,x_1) \in \mathbb {R}^{2}:0&amp;lt;t&amp;lt;T;\; \varphi _1(t) &amp;lt;x_1&amp;lt;\varphi _{2}(t) \bigr \rbrace  \times \prod _{i=1}^{N-1}{]0,b_i[} $    of ℝ N+1 , with Cauchy–Dirichlet boundary conditions, under some assumptions on the functionsϕ  1    $\varphi _1$    andϕ  2    $\varphi _2$   . The right-hand side term of the equation is taken inL  2    (  Q  )$L^{2}(Q)$   . The method used is based on the approximation of the domain  Q  by a sequence of sub-domains(   Q  n   )    $(Q_n)$    which can be transformed into regular domains. This work is an extension of the two space variables case studied in [Differ. Equ. Appl. 2 (2010), no. 2, 251–263].

Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝ N+1