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 paper deals with an inverse coefficient problem of simultaneously identifying the thermal conductivityk  ⁢   (  x  )k(x)    and radiative coefficientq  ⁢   (  x  )q(x)    in the 1D heat equationu  t   =(   k  ⁢   (  x  )   ⁢   u  x    )   x   -   q  ⁢   (  x  )   ⁢  uu_{t}=(k(x)u_{x})_{x}-q(x)u    from the most available Dirichlet and Neumann boundary measured outputs. The Neumann-to-Dirichlet and Neumann-to-Neumann operatorsΦ  ⁢   [  k  ,  q  ]   ⁢   (  t  )    :=   u  ⁢   (  ℓ  ,  t  ;  k  ,  q  )\Phi[k,q](t):=u(\ell,t;k,q)   ,Ψ  ⁢   [  k  ,  q  ]   ⁢   (  t  )    :=   -   k  ⁢   (  0  )   ⁢   u  x   ⁢   (  0  ,  t  ;  k  ,  q  )\Psi[k,q](t):=-k(0)u_{x}(0,t;k,q)    are introduced, and main properties of these operators are derived. Then the Tikhonov functional

Simultaneously identifying the thermal conductivity and radiative coefficient in heat equation from Dirichlet and Neumann boundary measured outputs