Nonlinear Volterra equation of parabolic type due to singular kernels (Q1332153)
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scientific article; zbMATH DE number 635869
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear Volterra equation of parabolic type due to singular kernels |
scientific article; zbMATH DE number 635869 |
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Nonlinear Volterra equation of parabolic type due to singular kernels (English)
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13 August 1995
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The author studies an integral equation of the form \[ u_ t (t,x) = \int^ t_ 0 k(t - s) \bigl( \sigma (u_ x) \bigr)_ x (s,x)ds + f(t,x) \] with a nonincreasing convex kernel \(k\) and \(\sigma\) increasing. Such equations occur in viscoelasticity. Sufficient conditions for the global existence of a strong solution are given. Sufficiently smooth solutions will be unique.
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nonlinear Volterra equation of parabolic type
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singular kernels
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nonincreasing convex kernel
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viscoelasticity
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strong solution
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smooth solutions
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