On the viscosity solutions to a degenerate parabolic differential equation
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0427-1 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0427-1 | ||
| 245 | 0 | 0 | |a On the viscosity solutions to a degenerate parabolic differential equation |h [Elektronische Daten] |c [Tilak Bhattacharya, Leonardo Marazzi] |
| 520 | 3 | |a In this work, we study positive viscosity solutions of the doubly nonlinear degenerate parabolic equation $$\varDelta _\infty \phi =(\phi ^3)_t=3\phi ^2\phi _t$$ Δ ∞ ϕ = ( ϕ 3 ) t = 3 ϕ 2 ϕ t in $$\varOmega \times (0,T)$$ Ω × ( 0 , T ) , where $$\varOmega \subset {\mathbb {R}}^n$$ Ω ⊂ R n is a bounded domain. Here, $$\varDelta _\infty $$ Δ ∞ is the infinity Laplacian. We prove a comparison principle, existence of continuous positive solutions, and some results regarding long-time asymptotic behavior. A maximum principle for $${\mathbb {R}}^n\times (0,T)$$ R n × ( 0 , T ) is also proven here. We adapt ideas and techniques described in Crandall and Ishii (Differ Integral Equ 3(6):1001-1014, 1990) and Crandall et al. (Bull Am Math Soc 27:1-67, 1992). | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Infinity Laplacian |2 nationallicence | |
| 690 | 7 | |a Degenerate parabolic |2 nationallicence | |
| 690 | 7 | |a Viscosity solutions |2 nationallicence | |
| 700 | 1 | |a Bhattacharya |D Tilak |u Department of Mathematics, Western Kentucky University, 42101, Bowling Green, KY, USA |4 aut | |
| 700 | 1 | |a Marazzi |D Leonardo |u Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1423-1454 |x 0373-3114 |q 194:5<1423 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0427-1 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0427-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bhattacharya |D Tilak |u Department of Mathematics, Western Kentucky University, 42101, Bowling Green, KY, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Marazzi |D Leonardo |u Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1423-1454 |x 0373-3114 |q 194:5<1423 |1 2015 |2 194 |o 10231 | ||
| 986 | |a SWISSBIB |b 605496471 | ||