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A singular abstract cauchy problem.

J A Donaldson1

  • 1THE UNIVERSITY OF NEW MEXICO, ALBUQUERQUE.

Proceedings of the National Academy of Sciences of the United States of America
|June 1, 1970
PubMed
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This study presents a novel solution for a singular abstract Cauchy problem by relating it to a regular version. This approach yields a new solution for initial value problems in singular partial differential equations.

Area of Science:

  • Mathematics
  • Partial Differential Equations
  • Functional Analysis

Background:

  • Singular abstract Cauchy problems pose significant challenges in mathematical analysis.
  • Existing methods for solving these problems are often limited or complex.

Purpose of the Study:

  • To introduce a novel method for solving singular abstract Cauchy problems.
  • To demonstrate the applicability of this method to singular partial differential equations.

Main Methods:

  • The core method involves transforming the singular problem into a regular abstract Cauchy problem.
  • The solution of the regular problem is then adapted to solve the original singular problem.

Main Results:

  • A new, explicit solution is derived for the considered singular abstract Cauchy problem.

Related Experiment Videos

  • This method provides a new solution for the initial value problem of a class of singular partial differential equations.

    • Conclusions:

    • The proposed technique offers an effective way to handle singular abstract Cauchy problems.
    • The findings contribute to the theory and application of singular partial differential equations.