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Global Existence of Solutions of Volterra Integrodifferential Equations of Parabolic Type

โœ Scribed by G. Gripenberg

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
285 KB
Volume
102
Category
Article
ISSN
0022-0396

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โœฆ Synopsis

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 (\sup \left{\sigma^{\prime}(p)\right} / \inf \left{\sigma^{\prime}(p)\right}<1+2 \kappa\left(\sqrt{\kappa^{2}+1}+\kappa\right)).

1993 Academic Press. Inc

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