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Global in time existence of small solutions of non‐linear thermoviscoelastic equations
Author(s) -
Shibata Yoshihiro
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670181104
Subject(s) - mathematics , constant (computer programming) , bounded function , a priori and a posteriori , multiplicative function , mathematical analysis , domain (mathematical analysis) , existence theorem , initial value problem , a priori estimate , philosophy , epistemology , computer science , programming language
We prove a global in time existence theorem of classical solutions of the initial boundary value problem for a non‐linear thermoviscoelastic equation in a bounded domain for very smooth initial data, external forces and heat supply which are very close to a specific constant equilibrium state. Our proof is a combination of a local in time existence theorem and some a priori estimates of local in time solutions. Such a priori estimates are proved basically for suitable linear problems by using some multiplicative techniques. An exponential stability of the constant equilibrium state also follows from our proof of the existence and regularity theorems.