Titlebook: Optimal Impulsive Control for Cancer Therapy; João P. Belfo,João M. Lemos Book 2021 The Author(s), under exclusive license to Springer Nat

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Stability of Spikes for the Gierer-Meinhardt System in One Dimension,. We will show that symmetric spikes in one dimension may be stable or unstable. Asymmetric spikes in one dimension are always unstable, however they may be metastable. Large eigenvalues of unity order are studied by nonlocal eigenvalue problems, small eigenvalues are investigated by a projection similar to Liapunov-Schmidt reduction.