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Some local estimates and a uniqueness result for the entire biharmonic heat equation

Journal Article


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Abstract


  • We consider smooth solutions to the biharmonic heat equation on ℝn × [0,T] for which the square of the Laplacian at time t is globally bounded from above by k0/t for some k0 in ℝ+, for all t ∈ [0,T]. We prove local, in space and time, estimates for such solutions. We explain how these estimates imply uniqueness of smooth solutions in this class.

Publication Date


  • 2016

Citation


  • Simon, M. & Wheeler, G. (2016). Some local estimates and a uniqueness result for the entire biharmonic heat equation. Advances in Calculus of Variations, 9 (1), 77-99.

Scopus Eid


  • 2-s2.0-84954226328

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6029&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5002

Number Of Pages


  • 22

Start Page


  • 77

End Page


  • 99

Volume


  • 9

Issue


  • 1

Place Of Publication


  • Germany

Abstract


  • We consider smooth solutions to the biharmonic heat equation on ℝn × [0,T] for which the square of the Laplacian at time t is globally bounded from above by k0/t for some k0 in ℝ+, for all t ∈ [0,T]. We prove local, in space and time, estimates for such solutions. We explain how these estimates imply uniqueness of smooth solutions in this class.

Publication Date


  • 2016

Citation


  • Simon, M. & Wheeler, G. (2016). Some local estimates and a uniqueness result for the entire biharmonic heat equation. Advances in Calculus of Variations, 9 (1), 77-99.

Scopus Eid


  • 2-s2.0-84954226328

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6029&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5002

Number Of Pages


  • 22

Start Page


  • 77

End Page


  • 99

Volume


  • 9

Issue


  • 1

Place Of Publication


  • Germany