On the nonexistence of globally bounded solutions to initial-history value problems for integrodifferential equations†

DOI10.1080/00036818108839351zbMath0492.45011OpenAlexW4256145552WikidataQ58244049 ScholiaQ58244049MaRDI QIDQ3954323

Frederick Bloom

Publication date: 1981

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036818108839351

zbMATH Keywords

globally bounded solutionsill-posed initial-history boundary value problems

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Asymptotics of solutions to integral equations (45M05) Electromagnetic theory (general) (78A25) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99)

Cites Work

• Linear functional electromagnetic constitutive relations and plane waves in a hemihedral isotropic material
• Growth estimates for solutions to initial-boundary value problems in viscoelasticity
• Growth estimates for electric displacement fields and bounds for constitutive constants in the Maxwell-Hopkinson theory of dielectrics
• Dynamical systems and stability
• Stability in linear elasticity
• Asymptotic stability in viscoelasticity
• Continuous dependence on data for solutions of partial differential equations with a prescribed bound
• Bounds for Solutions to a Class of Integro-differential Equations Associated with a Theory of Rigid Nonconducting Material Dielectrics
• Stability and growth estimates for Volterra integrodifferential equations in Hilbert space

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