Regularity of the free boundary for a parabolic cooperative system

G. Aleksanyan; M. Fotouhi; H. Shahgholian; G. S. Weiss

doi:10.1007/s00526-022-02244-1

Regularity of the free boundary for a parabolic cooperative system

G. Aleksanyan
, M. Fotouhi
, H. Shahgholian^*
, G. S. Weiss

^*Corresponding author for this work

Research output: Journal Publication › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we study the following parabolic system Δu-∂tu=|u|q-1uχ{|u|>0},u=(u1,⋯,um),with free boundary ∂{ | u| > 0 }. For 0 ≤ q< 1 , we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C¹^,^α in space directions and half-Lipschitz in the time direction.

Original language	English
Article number	124
Journal	Calculus of Variations and Partial Differential Equations
Volume	61
Issue number	4
DOIs	https://doi.org/10.1007/s00526-022-02244-1
Publication status	Published - Aug 2022
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00526-022-02244-1

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title = "Regularity of the free boundary for a parabolic cooperative system",

abstract = "In this paper we study the following parabolic system Δu-∂tu=|u|q-1uχ\{|u|>0\},u=(u1,⋯,um),with free boundary ∂\{ | u| > 0 \}. For 0 ≤ q< 1 , we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C1,α in space directions and half-Lipschitz in the time direction.",

author = "G. Aleksanyan and M. Fotouhi and H. Shahgholian and Weiss, \{G. S.\}",

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AU - Aleksanyan, G.

AU - Fotouhi, M.

AU - Shahgholian, H.

AU - Weiss, G. S.

PY - 2022/8

Y1 - 2022/8

N2 - In this paper we study the following parabolic system Δu-∂tu=|u|q-1uχ{|u|>0},u=(u1,⋯,um),with free boundary ∂{ | u| > 0 }. For 0 ≤ q< 1 , we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C1,α in space directions and half-Lipschitz in the time direction.

AB - In this paper we study the following parabolic system Δu-∂tu=|u|q-1uχ{|u|>0},u=(u1,⋯,um),with free boundary ∂{ | u| > 0 }. For 0 ≤ q< 1 , we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C1,α in space directions and half-Lipschitz in the time direction.

UR - https://www.scopus.com/pages/publications/85129534949

U2 - 10.1007/s00526-022-02244-1

DO - 10.1007/s00526-022-02244-1

M3 - Article

AN - SCOPUS:85129534949

SN - 0944-2669

VL - 61

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

M1 - 124

ER -

Regularity of the free boundary for a parabolic cooperative system

Abstract

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