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finite speed of disturbance

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Finite speed of disturbance for the nonlinear Schrödinger equation
Part of
- Partial differential equations
- Equations of mathematical physics and other areas of application
Simão Correia
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 6 / December 2019

Published online by Cambridge University Press:

27 December 2018, pp. 1405-1419

Print publication:

December 2019
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We consider the Cauchy problem for the nonlinear Schrödinger equation on the whole space. After introducing a weaker concept of finite speed of propagation, we show that the concatenation of initial data gives rise to solutions whose time of existence increases as one translates one of the initial data. Moreover, we show that, given global decaying solutions with initial data u0, v0, if |y| is large, then the concatenated initial data u0 + v0(· − y) gives rise to globally decaying solutions.