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Monotonicity method for the complex Ginzburg–Landau equation, including smoothing effect

✍ Scribed by N. Okazawa; T. Yokota


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
431 KB
Volume
47
Category
Article
ISSN
0362-546X

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Global existence of unique strong solutions is established for the complex Ginzburg-Landau equation The key is a new inequality in monotonicity methods. It is based on the sectorial estimates of -in L p+1 and the nonlinear operator u → u p-1 u appearing in the equation. The key inequality also yiel

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In this work, the authors first show the existence of global attractors A ε for the following lattice complex Ginzburg-Landau equation: and A 0 for the following lattice Schrödinger equation: Then they prove that the solutions of the lattice complex Ginzburg-Landau equation converge to that of the