TY - JOUR

T1 - ОБ ОДНОЙ ЗАДАЧЕ О НАГРЕВЕ ПРОВОДНИКА

AU - Pavlenko, V. N.

AU - Potapov, D. K.

N1 - Funding Information: The research was funded by RFBR and Chelyabinsk Region, project number 20-41-740003. Publisher Copyright: © 2021 The authors.

PY - 2021

Y1 - 2021

N2 - Kuiper’s problem on conductor heating in a uniform electric field of intensity √λ with a positive parameter λ is considered. The conductor temperature distribution is a solution to the Dirichlet problem with homogeneous initial data in a bounded domain for a quasilinear elliptic equation with a discontinuous nonlinearity and a parameter. The heat-conductivity coefficient depends on the spatial variable and temperature, and the specific electric conductivity has discontinuities with respect to the phase variable. The existence of a continuum of generalized positive solutions that connects (0, 0) to ∞ is proved by a topological method. A sufficient condition is obtained for such solutions to be semiregular. Compared to the papers of H.J. Kuiper and K.C. Chang, the restrictions on the discontinuous nonlinearity (the specific electric conductivity) are weaken.

AB - Kuiper’s problem on conductor heating in a uniform electric field of intensity √λ with a positive parameter λ is considered. The conductor temperature distribution is a solution to the Dirichlet problem with homogeneous initial data in a bounded domain for a quasilinear elliptic equation with a discontinuous nonlinearity and a parameter. The heat-conductivity coefficient depends on the spatial variable and temperature, and the specific electric conductivity has discontinuities with respect to the phase variable. The existence of a continuum of generalized positive solutions that connects (0, 0) to ∞ is proved by a topological method. A sufficient condition is obtained for such solutions to be semiregular. Compared to the papers of H.J. Kuiper and K.C. Chang, the restrictions on the discontinuous nonlinearity (the specific electric conductivity) are weaken.

KW - conductor heating

KW - continuum of positive solutions

KW - discontinuous nonlinearity

KW - Kuiper’s problem

KW - quasilinear elliptic equation

KW - semiregular solution

KW - topological method

UR - http://www.scopus.com/inward/record.url?scp=85128126228&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/6d0688e4-f80c-3131-8db9-273acc9527ac/

U2 - 10.47475/2500-0101-2021-16304

DO - 10.47475/2500-0101-2021-16304

M3 - статья

AN - SCOPUS:85128126228

VL - 6

SP - 299

EP - 311

JO - Chelyabinsk Physical and Mathematical Journal

JF - Chelyabinsk Physical and Mathematical Journal

SN - 2500-0101

IS - 3

ER -