Existence of Global Weak Solutions for Coupled Thermoelasticity with Barber's Heat Exchange Condition
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M. Bień
Abstract
The existence of global weak solutions for coupled thermoelasticity with the nonlinear contact boundary condition and Barber's heat exchange condition is proved via the Faedo-Galerkin, monotonicity and compactness methods. Some a priori bounds obtained with Gronwalls inequality in connection with the embedding and trace theorems lead to accomplishing a generalization of our previous study [Bień, Math. Methods Appl. Sci. 19: 1265–1277, 1996]. The heat-exchange coefficient associated with Barber's heat exchange condition is dependent only on the normal displacement. This dependence is described by a bounded Lipschitz function. Moreover, this study is some extension of works due to Andrews et al. [Shi, Shillor, Wright, Appl. Math. Optim. 28: 11–48, 1993] and Elliot et al. [Tang, Nonlinear Anal. 23: 883–898, 1994].
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Articles in the same Issue
- Critical Cardinalities and Additivity Properties of Combinatorial Notions of Smallness
- Existence of Global Weak Solutions for Coupled Thermoelasticity with Barber's Heat Exchange Condition
- A Priori Solution Estimates for Nonlinear Vector Integral Equations
- On a Boundary Value Problem for a Nonlocal Elliptic Equation
- On Noncoercive Elliptic Problems with Discontinuities
- Some Nonlinear Problems in Hyperconvex Metric Spaces
- Linearly Invariant Families of Holomorphic Mappings in . Transition to Other Dimensions
- On Continuous Selection Problems for Multivalued Mappings with the Local Intersection Property in Hyperconvex Metric Spaces
- Second-Order Characterizations of Convex and Pseudoconvex Functions
- On Marczewski-Burstin Representations of Algebras and Ideals
- New and Generalized Convergence Conditions for the Newton-Kantorovich Method