The uniqueness of the solution of a nonlinear heat conduction problem under Hölder’s continuity condition

0520539 - MÚ 2021 RIV US eng J - Journal Article
Křížek, Michal
The uniqueness of the solution of a nonlinear heat conduction problem under Hölder’s continuity condition.
Applied Mathematics Letters. Roč. 103, May (2020), č. článku 106214. ISSN 0893-9659. E-ISSN 1873-5452
R&D Projects: GA ČR(CZ) GA18-09628S; GA ČR(CZ) GA20-01074S
Institutional support: RVO:67985840
Keywords : weak solution * nonlinear heat conduction * heat transfer coefficient * Hölder continuity
OECD category: Pure mathematics
Impact factor: 4.055, year: 2020
Method of publishing: Limited access
https://doi.org/10.1016/j.aml.2020.106214

We investigate a stationary nonlinear heat conduction problem in which heat conductivities depend on temperature. It is known that such problem need not have a unique solution even when the conductivity coefficients are continuous. In this paper we prove that for 1/2-Hölder continuous coefficients the uniqueness of the weak solution is guaranteed.
Permanent Link: http://hdl.handle.net/11104/0305197