# 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…

## 2 Citations

### On a Multivalued Differential Equation with Nonlocality in Time

- Mathematics
- 2019

The initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a…

### Ju n 20 19 On a multivalued di ff erential equation with nonlocality in time 1

- Mathematics
- 2019

The initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a…

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