Unidirectional evolution equations of diffusion type

Goro Akagi, Masato Kimura

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


This paper is concerned with the uniqueness, existence, partial smoothing effect, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in Damage Mechanics due to the strong irreversibility of crack propagation or damage evolution. The existence of solutions is proved in an L2-framework by employing a backward Euler scheme and by introducing a new method of a priori estimates based on a reduction of discretized equations to variational inequalities of obstacle type and by developing a regularity theory for such obstacle problems. The novel discretization argument will be also applied to prove the comparison principle as well as to investigate the long-time behavior of solutions.

Original languageEnglish
Pages (from-to)1-43
Number of pages43
JournalJournal of Differential Equations
Issue number1
Publication statusPublished - 2019 Jan 5


  • Damage mechanics
  • Discretization
  • Regularity
  • Subdifferential calculus
  • Unidirectional diffusion equation
  • Variational inequality of obstacle type

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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