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Global solution to the Cauchy problem in non‐linear hyperbolic thermoelasticity
Author(s) -
Gawinecki Jerzy
Publication year - 1992
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.1670150402
Subject(s) - mathematics , thermoelastic damping , initial value problem , hyperbolic partial differential equation , mathematical analysis , cauchy problem , partial differential equation , space (punctuation) , cauchy distribution , thermal , linguistics , philosophy , physics , meteorology
We prove the existence of global solutions for small data to the initial value problem for the non‐linear hyperbolic system of partial differential equations describing a thermoelastic medium in a three‐dimensional space under the assumption that the coefficients in the non‐linear terms are smooth functions of their arguments and behave like 0(∣η∣ k 0) for k 0 ≥ 2 near the origin. The asymptotic behaviour of the solution as t → ∞ is also described.