On integro‐differential inclusions with operator‐valued kernels
Copyright policy )On integro‐differential inclusions with operator‐valued kernels
AbstractWe study integro‐differential inclusions in Hilbert spaces with operator‐valued kernels and give sufficient conditions for the well‐posedness. We show that several types of integro‐differential equations and inclusions are covered by the class of evolutionary inclusions, and we therefore give criteria for the well‐posedness within this framework. As an example, we apply our results to the equations of visco‐elasticity and to a class of nonlinear integro‐differential inclusions describing phase transition phenomena in materials with memory. Copyright © 2014 John Wiley & Sons, Ltd.
causality, linear material laws, Initial-boundary value problems for systems of nonlinear first-order PDEs, integro-differential equations, Functional Analysis (math.FA), Mathematics - Functional Analysis, Integro-partial differential equations, Mathematics - Analysis of PDEs, integro-differential inclusions, well-posedness, FOS: Mathematics, evolutionary inclusions, Applications of functional analysis to differential and integral equations, Nonlinear evolution equations, Integro-differential operators, 35R09, 47G20, 35F61, 46N20, 47J35, Analysis of PDEs (math.AP)
causality, linear material laws, Initial-boundary value problems for systems of nonlinear first-order PDEs, integro-differential equations, Functional Analysis (math.FA), Mathematics - Functional Analysis, Integro-partial differential equations, Mathematics - Analysis of PDEs, integro-differential inclusions, well-posedness, FOS: Mathematics, evolutionary inclusions, Applications of functional analysis to differential and integral equations, Nonlinear evolution equations, Integro-differential operators, 35R09, 47G20, 35F61, 46N20, 47J35, Analysis of PDEs (math.AP)
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