On the maximum and comparison principles for a steady-state nonlinear heat conduction problem. (English) Zbl 1030.35061
A boundary value problem of elliptic type, which describes the stationary heat conduction in nonlinear, inhomogeneous and anisotropic media is considered. The matrix function of the above nonlinear problem depends on the unknown.
A comparison principle (which says that any rise of the density of heat sources determines a nondecreasing temperature) is obtained. As a consequence of the comparison principle, a maximum principle is established. A numerical example is considered.
A comparison principle (which says that any rise of the density of heat sources determines a nondecreasing temperature) is obtained. As a consequence of the comparison principle, a maximum principle is established. A numerical example is considered.
Reviewer: Ruxandra Stavre (Bucureşti)
MSC:
35J60 | Nonlinear elliptic equations |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35B50 | Maximum principles in context of PDEs |