Abstract
We consider the initial—boundary value problem for the hyperbolic partial differential equations of thermoelasticity theory for non-simple materials. The new approach is based on the fact that we consider the initial—boundary value problem for these equations with control for temperature. We formulate the control for termperature in the terms of maximal monotone set. Existence, uniqueness and regularity of the solution to this initial—boundary value problems are proved in Sobolev space. In our proof, we use the semigroup theory and the method of Hilbert space.
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Gawinecki, J., Kowalski, L. (1998). Mathematical Aspects of the Boundary Initial Value Problems for Thermoelasticity Theory of Non-simple Materials with Control for Temperature. In: Marti, K., Kall, P. (eds) Stochastic Programming Methods and Technical Applications. Lecture Notes in Economics and Mathematical Systems, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45767-8_23
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DOI: https://doi.org/10.1007/978-3-642-45767-8_23
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