Nonlinear Evolution Equations with Exponentially Decaying Memory: Existence via Time Discretisation, Uniqueness, and Stability

@article{Eikmeier2020NonlinearEE,
  title={Nonlinear Evolution Equations with Exponentially Decaying Memory: Existence via Time Discretisation, Uniqueness, and Stability},
  author={Andr{\'e} Eikmeier and Etienne Emmrich and Hans-Christian Kreusler},
  journal={Computational Methods in Applied Mathematics},
  year={2020},
  volume={20},
  pages={89 - 108}
}
Abstract The initial value problem for an evolution equation of type v ′ + A ⁢ v + B ⁢ K ⁢ v = f {v^{\prime}+Av+BKv=f} is studied, where A : V A → V A ′ {A:V_{A}\to V_{A}^{\prime}} is a monotone, coercive operator and where B : V B → V B ′ {B:V_{B}\to V_{B}^{\prime}} induces an inner product. The Banach space V A {V_{A}} is not required to be embedded in V B {V_{B}} or vice versa. The operator K incorporates a Volterra integral operator in time of convolution type with an exponentially decaying… 

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