Condition-dependent Hilbert Spaces for Steepest Descent and Application to the Tricomi Equation

@inproceedings{Montgomery2014ConditiondependentHS,
  title={Condition-dependent Hilbert Spaces for Steepest Descent and Application to the Tricomi Equation},
  author={Jason W. Montgomery},
  year={2014}
}
A steepest descent method is constructed for the general setting of a linear differential equation paired with uniqueness-inducing conditions which might yield a generally overdetermined system. The method differs from traditional steepest descent methods by considering the conditions when defining the corresponding Sobolev space. The descent method converges to the unique solution to the differential equation so that change in condition values is minimal. The system has a solution if and only… CONTINUE READING

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