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- W4378468611 abstract "<abstract><p>We study layered solutions in a one-dimensional version of the scalar Ginzburg-Landau equation that involves a mixture of a second spatial derivative and a fractional half-derivative, together with a periodically modulated nonlinearity. This equation appears as the Euler-Lagrange equation of a suitably renormalized fractional Ginzburg-Landau energy with a double-well potential that is multiplied by a 1-periodically varying nonnegative factor $ g(x) $ with $ int_0^1 frac{1}{g(x)} dx < infty. $ A priori this energy is not bounded below due to the presence of a nonlocal term in the energy. Nevertheless, through a careful analysis of a minimizing sequence we prove existence of global energy minimizers that connect the two wells at infinity. These minimizers are shown to be the classical solutions of the associated nonlocal Ginzburg-Landau type equation.</p></abstract>" @default.
- W4378468611 created "2023-05-27" @default.
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- W4378468611 date "2023-01-01" @default.
- W4378468611 modified "2023-09-26" @default.
- W4378468611 title "Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation" @default.
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- W4378468611 doi "https://doi.org/10.3934/mine.2023090" @default.
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