On the uniqueness and nonuniqueness of weak solutions of hyperbolic- parabolic Volterra equations (Q1316973)
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scientific article; zbMATH DE number 527363
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the uniqueness and nonuniqueness of weak solutions of hyperbolic- parabolic Volterra equations |
scientific article; zbMATH DE number 527363 |
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On the uniqueness and nonuniqueness of weak solutions of hyperbolic- parabolic Volterra equations (English)
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24 March 1994
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The author considers a nonlinear Volterra equation that occurs in viscoelasticity models and reduces to a wave equation or a diffusion equation for suitable choices of the kernel. He indicates conditions on the kernel and the nonlinearity under which the general equation has a unique weak solution, and conditions under which it has infinitely many weak solutions.
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hyperbolic-parabolic Volterra equations
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nonlinear Volterra equation
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viscoelasticity
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wave equation
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diffusion equation
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unique weak solution
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infinitely many weak solutions
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