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Infinity of solutions to initial‐boundary value problems for linear constant‐coefficient evolution PDEs on semi‐infinite intervals

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Non-uniqueness counter-examples of classical solutions highlight the complexities in initial-boundary value problems.
This approach utilizes complex-analytic techniques to analyze regularity and asymptotic behaviors near boundaries.
The proposed method applies rigorously to the heat equation and linear KdV equation, unveiling new uniqueness theorems.
Significance lies in its innovative algorithmic approach, which could reshape understanding of solution behaviors in PDEs.

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This communication demonstrates an algorithm for identifying non-unique solutions in linear PDEs, suggesting new insights into boundary behaviors.

Chatziafratis et al. (2025) studied this question.

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This communication demonstrates an algorithm for identifying non-unique solutions in linear PDEs, suggesting new insights into boundary behaviors.