Differential and Integral Equations

Evolution equations with nonlinear constitutive laws and memory effects

Albert Milani and Rainer Picard

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Evolution equations are considered as operator equations involving a sum of the time-derivative operator $ \partial _{0} $ regarded as a normal operator in a suitable Hilbert space setting and another fairly arbitrary spatial operator $ A$ acting in a Hilbert space $ H $. As an extension of the linear theory the case of a class of nonlinear constitutive laws with memory effects is considered.

Article information

Differential Integral Equations, Volume 15, Number 3 (2002), 327-344.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory 35R10: Partial functional-differential equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 78A25: Electromagnetic theory, general


Milani, Albert; Picard, Rainer. Evolution equations with nonlinear constitutive laws and memory effects. Differential Integral Equations 15 (2002), no. 3, 327--344. https://projecteuclid.org/euclid.die/1356060863

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