TY  - JOUR
AU  - Nguyen Anh Dao, null
AU  - Ildefonso Diaz, Jesus
AU  - Quan Ba Hong Nguyen, null
TI  - Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term
JF  - ADVANCED NONLINEAR STUDIES
J2  - ADV NONLINEAR STUD
VL  - 20
PY  - 2020
IS  - 2
SP  - 477
EP  - 502
PG  - 26
SN  - 1536-1365
DO  - 10.1515/ans-2020-2076
UR  - https://m2.mtmt.hu/api/publication/31416380
ID  - 31416380
AB  - We consider the high-dimensional equation partial derivative(t)u -Delta u(m) + u(-beta)chi({u>0}) = 0, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case. Besides the existence of a very weak solution u is an element of C([0, T]; L-delta(1)(Omega)), with u(-beta)chi({u>0}) is an element of L-1 ((0, T) x Omega), delta(x) = d(x, partial derivative Omega), we prove some pointwise gradient estimates for a certain range of the dimension N, m >= 1 and beta is an element of (0, m), mainly when the absorption dominates over the diffusion (1 <= m < 2 + beta ). In particular, a new kind of universal gradient estimate is proved when m + beta <= 2. Several qualitative properties (such as the finite time quenching phenomena and the finite speed of propagation) and the study of the Cauchy problem are also considered.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Jin, Chunhua
AU  - Yin, Jingxue
AU  - Zheng, Sining
TI  - Propagation profile of support for evolution p-Laplacian with convection in half space
JF  - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
J2  - J MATH ANAL APPL
VL  - 416
PY  - 2014
IS  - 2
SP  - 710
EP  - 723
PG  - 14
SN  - 0022-247X
DO  - 10.1016/j.jmaa.2014.02.064
UR  - https://m2.mtmt.hu/api/publication/25746542
ID  - 25746542
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Winkler, M
TI  - Infinite-time quenching in a fast diffusion equation with strong absorption
JF  - NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
J2  - NODEA-NONLINEAR DIFF
VL  - 16
PY  - 2009
IS  - 1
SP  - 41
EP  - 61
PG  - 21
SN  - 1021-9722
DO  - 10.1007/s00030-008-0052-z
UR  - https://m2.mtmt.hu/api/publication/21683395
ID  - 21683395
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Winkler, Michael
TI  - Nonuniqueness in the quenching problem
JF  - MATHEMATISCHE ANNALEN
J2  - MATH ANN
VL  - 339
PY  - 2007
IS  - 3
SP  - 559
EP  - 597
PG  - 39
SN  - 0025-5831
DO  - 10.1007/s00208-007-0123-1
UR  - https://m2.mtmt.hu/api/publication/25727647
ID  - 25727647
LA  - English
DB  - MTMT
ER  -