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Due to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour...
We present an existence result for an evolution equation with a nonlinear operator, which is a composition of two monotone mappings. The first monotone mapping is a subdifferential of the indicator function of some convex set while the other is constructed as the Nemyckii operator of a monotone function. Such equations arise from the mathematical models, which describe piezoelectric material behavior...
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