For a two-layer diffusive energy balance climate model, finite-time blow-up occurs if atmospheric absorptivity exceeds 2, while global existence of solutions and a global attractor hold for absorptivity in (0,2).
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The slow component converges strongly to an effective stochastic fractional Schrödinger equation obtained by averaging the coupling term over the unique invariant measure of the frozen fast dynamics.
Supplies a counterexample showing inconsistencies in Lavrentiev's original proof and gives a new complete proof that the Lavrentiev phenomenon is absent in one dimension under the stated conditions.
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Comparison principles and long time behavior for a diffusive Energy Balance Model with vertical resolution
For a two-layer diffusive energy balance climate model, finite-time blow-up occurs if atmospheric absorptivity exceeds 2, while global existence of solutions and a global attractor hold for absorptivity in (0,2).
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Averaging principle for a slow-fast stochastic nonlinear fractional Schr\"odinger equation
The slow component converges strongly to an effective stochastic fractional Schrödinger equation obtained by averaging the coupling term over the unique invariant measure of the frozen fast dynamics.
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Revisiting the Lavrentiev Phenomenon in One Dimension
Supplies a counterexample showing inconsistencies in Lavrentiev's original proof and gives a new complete proof that the Lavrentiev phenomenon is absent in one dimension under the stated conditions.