Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor

DOI10.1007/BF01759998zbMath0769.35059OpenAlexW2028738275MaRDI QIDQ1210146

Publication date: 16 May 1993

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01759998

zbMATH Keywords

initial-boundary value problem Faedo-Galerkin method nonlinear elliptic-parabolic system

Mathematics Subject Classification ID

Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).

Related Items (31)

New superconvergence estimates of FEM for time-dependent Joule heating problem ⋮ A B-spline finite element method for the thermistor problem with the modified electrical conductivity ⋮ UNIFORM BMO ESTIMATE OF PARABOLIC EQUATIONS AND GLOBAL WELL-POSEDNESS OF THE THERMISTOR PROBLEM ⋮ Finite element convergence analysis for the thermoviscoelastic Joule heating problem ⋮ Capacity solution for a perturbed nonlinear coupled system ⋮ Existence of capacity solution for a nonlocal thermistor problem in Musielak-Orlicz-Sobolev spaces ⋮ Superconvergence analysis of finite element method for time-fractional thermistor problem ⋮ Existence of weak solutions of an unsteady thermistor system with \(p\)-Laplacian type equation ⋮ Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem ⋮ On certain doubly non-uniformly and singular non-uniformly elliptic systems. ⋮ Superconvergent estimates of conforming finite element method for nonlinear time‐dependent Joule heating equations ⋮ Numerical solutions of the thermistor problem with a ramp electrical conductivity. ⋮ Regularity of solutions of the thermistor problem ⋮ Existence of three positive solutions to some \(p\)-Laplacian boundary value problems ⋮ Optimal error analysis of Galerkin FEMs for nonlinear Joule heating equations ⋮ On the existence of weak solutions of an unsteady \(p\)-Laplace thermistor system with strictly monotone electrical conductivities ⋮ Existence of a solution for a thermoelectric model with several phase changes and a Carathéodory thermal conductivity ⋮ Stability and convergence of fully discrete Galerkin FEMs for the nonlinear thermistor equations in a nonconvex polygon ⋮ On an induction-conduction PDEs system in the harmonic regime ⋮ Numerical solutions of the thermistor problem by spline finite elements ⋮ Finite element solution of the thermistor problem with a ramp electrical conductivity ⋮ Superconvergence analysis of nonconforming FEM for nonlinear time-dependent thermistor problem ⋮ Finite element approaches to the PTC thermistor problem ⋮ A heat balance integral solution of the thermistor problem with a modified electrical conductivity ⋮ A Finite Element Model for the Time-Dependent Joule Heating Problem ⋮ Optimal error estimates of a lowest-order Galerkin-mixed FEM for the thermoviscoelastic Joule heating equations ⋮ Analytic regimes with peaking in the thermistor problem ⋮ Linearly implicit finite element methods for the time-dependent Joule heating problem ⋮ Regularity Results for a Nonlinear Elliptic-Parabolic System with Oscillating Coefficients ⋮ An Elliptic System Related to the Stationary Thermistor Problem ⋮ Unconditional optimal error estimates of BDF-Galerkin FEMs for nonlinear thermistor equations

Cites Work

This page was built for publication: Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor