The Gross-Pitaewsky equation with time and space dependent coefficients

Q: What type of study is this?

This is a Quantitative Study study.

Fayuan Lai

doi:10.48550/arxiv.2509.06001

September 7, 2025Open Access

The Gross-Pitaewsky equation with time and space dependent coefficients

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Key Points

The study focuses on the existence of solutions in a parabolic reaction-diffusion context, showing potential for blow-up or decay.
Key properties of the gross-pitaevskii equation under evolving coefficients are examined, considering various initial conditions.
Using techniques for parabolic systems, the analysis accommodates time and space variability in coefficients and their effects.
This research contributes to understanding the behavior of nonlinear equations, highlighting challenges and future research avenues.

Implication

Analysis reveals solutions to the parabolic reaction-diffusion system in multiple contexts, indicating complex behavior.

Abstract

In this work we study the existence and other properties of a solution of a parabolic reaction-diffusion system, that is the the Gross-Pitaevskii equation with time and space dependent coefficients, that could blow up or vanish asymptotically in time, with an initial data not necessarily segregated.

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Cite This Study

Fayuan Lai (2025) studied this question.

synapsesocial.com/papers/68ebffcfdef9fcb308ff25a7 https://doi.org/10.48550/arxiv.2509.06001

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The Gross-Pitaewsky equation with time and space dependent coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

The Gross-Pitaewsky equation with time and space dependent coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

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