Global Existence of Solutions of Volterr
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G. Gripenberg
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Article
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1993
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Elsevier Science
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English
β 285 KB
Sufficient conditions for the global existence of a strong solution of the equation \(u_{t}(t, x)=\int_{0}^{i} k(t-s) \sigma\left(u_{x}(s, x)\right)_{x} d s+f(t, x)\) are given. The kernel \(k\) satisfies \(9 \hat{k}(z) \geqslant\) \(\kappa|\exists \hat{k}(z)|\) and \(\sigma\) is increasing with \(\