Global-in-Time Regular Unique Solutions with Positive Temperature to One-Dimensional Thermoelasticity
Piotr Michał Bies, Tomasz Cieślak
Abstract
We construct a unique regular solution to the minimal nonlinear system of one-dimensional thermoelasticity. The obtained solution has a positive temperature. Our approach is based on an estimate, using the Fisher information, which seems completely new in this context. It is combined with a recent inequality in T. Cieślak, M. Fuest, K. Hajduk, and M. Sierżȩga, On Existence of Global Solutions for the 3D Chemorepulsion System, preprint, arXiv:2303.09620, 2023. and embeddings, which allow us to obtain a new energy estimate. The latter is used in a half-Galerkin procedure yielding global solutions. The uniqueness and further regularity of such solutions are obtained.
Topics & Concepts
PreprintUniquenessMathematicsGalerkin methodContext (archaeology)Nonlinear systemMathematical analysisApplied mathematicsEnergy (signal processing)PhysicsPaleontologyBiologyQuantum mechanicsStatisticsGas Dynamics and Kinetic TheoryNavier-Stokes equation solutionsComputational Fluid Dynamics and Aerodynamics