TY  - JOUR
AU  - Hernandez-Berrnejo, Benito
AU  - Gabriel Iagar, Razvan
AU  - Gordoa, Pilar R.
AU  - Pickering, Andrew
AU  - Sanchez, Ariel
TI  - Equivalence and finite time blow-up of solutions and interfaces for two nonlinear diffusion equations
JF  - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
J2  - J MATH ANAL APPL
VL  - 482
PY  - 2020
IS  - 1
PG  - 16
SN  - 0022-247X
DO  - 10.1016/j.jmaa.2019.123503
UR  - https://m2.mtmt.hu/api/publication/31457089
ID  - 31457089
AB  - In this work, we construct a transformation between the solutions to the following reaction-convection-diffusion equationpartial derivative(t)u = (u(m))(xx) a(x)(u(m))(x) b(x)u(m),posed for x is an element of, t >= 0 and m > 1, where a, b are two continuous real functions, and the solutions to the nonhomogeneous diffusion equation of porous medium typef(y)partial derivative tau theta = (theta(m))(yy),posed in the half-line y is an element of [0, infinity) with tau >= 0, m > 1 and suitable density functions f (y). We apply this correspondence to the case of constant coefficients a(x) =1 and b(x) = K > 0. For this case, we prove that compactly supported solutions to the first equation blow up in finite time, together with their interfaces, as x -> -infinity. We then establish the large time behavior of solutions to a homogeneous Dirichlet problem associated to the first equation on a bounded interval. We also prove a finite time blow-up of the interfaces for compactly supported solutions to the second equation when f(y) = y(-gamma) with gamma > 2. (C) 2019 Elsevier Inc. All rights reserved.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Grillo, Gabriele
AU  - Muratori, Matteo
AU  - Luis Vazquez, Juan
TI  - The porous medium equation on Riemannian manifolds with negative curvature: the superquadratic case
JF  - MATHEMATISCHE ANNALEN
J2  - MATH ANN
VL  - 373
PY  - 2019
IS  - 1-2
SP  - 119
EP  - 153
PG  - 35
SN  - 0025-5831
DO  - 10.1007/s00208-018-1680-1
UR  - https://m2.mtmt.hu/api/publication/30905939
ID  - 30905939
AB  - We study the long-time behaviour of nonnegative solutions of the Porous Medium Equation posed on Cartan-Hadamard manifolds having very large negative curvature, more precisely when the sectional or Ricci curvatures diverge at infinity more than quadratically in terms of the geodesic distance to the pole. We find an unexpected separate-variable behaviour that reminds one of Dirichlet problems on bounded Euclidean domains. As a crucial step, we prove existence of solutions to a related sublinear elliptic problem, a result of independent interest. Uniqueness of solutions vanishing at infinity is also shown, along with comparison principles, both in the parabolic and in the elliptic case. Our results complete previous analyses of the porous medium equation flow on negatively curved Riemannian manifolds, which were carried out first for the hyperbolic space and then for general Cartan-Hadamard manifolds with a negative curvature having at most quadratic growth. We point out that no similar analysis seems to exist for the linear heat flow. We also translate such results into some weighted porous medium equations in the Euclidean space having special weights.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Grebenev, V N
AU  - Nazarenko, S V
AU  - Medvedev, S B
TI  - Complementary remarks to properties of the energy spectrum in Leith's model of turbulence
JF  - ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
J2  - ZAMM-Z ANGEW MATH ME
VL  - 97
PY  - 2017
IS  - 6
SP  - 664
EP  - 669
PG  - 6
SN  - 0044-2267
DO  - 10.1002/zamm.201600060
UR  - https://m2.mtmt.hu/api/publication/26729745
ID  - 26729745
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Punzo, Fabio
AU  - Strani, Marta
TI  - Dirichlet Boundary Conditions for Degenerate and Singular Nonlinear Parabolic Equations
JF  - POTENTIAL ANALYSIS
J2  - POTENTIAL ANAL
VL  - 47
PY  - 2017
IS  - 2
SP  - 151
EP  - 168
PG  - 18
SN  - 0926-2601
DO  - 10.1007/s11118-016-9611-9
UR  - https://m2.mtmt.hu/api/publication/26729744
ID  - 26729744
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Gabriel, Iagar Razvan
AU  - Sanchez, Ariel
TI  - Asymptotic behavior for the critical nonhomogeneous porous medium equation in low dimensions
JF  - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
J2  - J MATH ANAL APPL
VL  - 439
PY  - 2016
IS  - 2
SP  - 843
EP  - 863
PG  - 21
SN  - 0022-247X
DO  - 10.1016/j.jmaa.2016.03.015
UR  - https://m2.mtmt.hu/api/publication/26002858
ID  - 26002858
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Wang, Y
AU  - Xiang, Z
TI  - The interfaces of an inhomogeneous non-Newtonian polytropic filtration equation with convection
JF  - IMA JOURNAL OF APPLIED MATHEMATICS
J2  - IMA J APPL MATH
VL  - 80
PY  - 2015
IS  - 2
SP  - 354
EP  - 375
PG  - 22
SN  - 0272-4960
DO  - 10.1093/imamat/hxt043
UR  - https://m2.mtmt.hu/api/publication/25497394
ID  - 25497394
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Punzo, F
TI  - Uniqueness and non-uniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds
JF  - ASYMPTOTIC ANALYSIS
J2  - ASYMPTOTIC ANAL
VL  - 79
PY  - 2012
IS  - 3-4
SP  - 273
EP  - 301
PG  - 29
SN  - 0921-7134
DO  - 10.3233/ASY-2012-1098
UR  - https://m2.mtmt.hu/api/publication/23006056
ID  - 23006056
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Punzo, F
TI  - Uniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolution
JF  - ANNALI DI MATEMATICA PURA ED APPLICATA
J2  - ANN MAT PUR APPL
VL  - 191
PY  - 2012
IS  - 2
SP  - 311
EP  - 338
PG  - 28
SN  - 0373-3114
DO  - 10.1007/s10231-011-0185-2
UR  - https://m2.mtmt.hu/api/publication/23006055
ID  - 23006055
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Punzo, F
TI  - On support of solutions to singular nonlinear parabolic equations in bounded domains
JF  - INTERFACES AND FREE BOUNDARIES
J2  - INTERFACE FREE BOUND
VL  - 13
PY  - 2011
IS  - 3
SP  - 397
EP  - 410
PG  - 14
SN  - 1463-9963
DO  - 10.4171/IFB/264
UR  - https://m2.mtmt.hu/api/publication/23006057
ID  - 23006057
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Punzo, F
AU  - Tesei, A
TI  - On a Semilinear Parabolic Equation with Inverse-Square Potential
JF  - RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI
J2  - REND LINCEI-MAT APPL
VL  - 21
PY  - 2010
IS  - 4
SP  - 359
EP  - 396
PG  - 38
SN  - 1120-6330
DO  - 10.4171/RLM/578
UR  - https://m2.mtmt.hu/api/publication/23006058
ID  - 23006058
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Guedda, Mohammed
TI  - Multiple positive solutions to a singular boundary value problem for a superlinear Emden-Fowler equation
JF  - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
J2  - J MATH ANAL APPL
VL  - 352
PY  - 2009
IS  - 1
SP  - 259
EP  - 270
PG  - 12
SN  - 0022-247X
DO  - 10.1016/j.jmaa.2008.05.028
UR  - https://m2.mtmt.hu/api/publication/25687099
ID  - 25687099
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Punzo, F
TI  - Uniqueness and non-uniqueness of bounded solutions to singular nonlinear parabolic equations
JF  - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
J2  - NONLINEAR ANAL-THEOR
VL  - 70
PY  - 2009
IS  - 8
SP  - 3020
EP  - 3029
PG  - 10
SN  - 0362-546X
DO  - 10.1016/j.na.2008.12.025
UR  - https://m2.mtmt.hu/api/publication/23006059
ID  - 23006059
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Kamin, S
AU  - Pozio, MA
AU  - Tesei, A
TI  - ADMISSIBLE CONDITIONS FOR PARABOLIC EQUATIONS DEGENERATING AT INFINITY
JF  - ST PETERSBURG MATHEMATICAL JOURNAL
J2  - ST PETERSB MATH J+
VL  - 19
PY  - 2008
IS  - 2
SP  - 239
EP  - 251
PG  - 13
SN  - 1061-0022
DO  - 10.1090/S1061-0022-08-00996-5
UR  - https://m2.mtmt.hu/api/publication/23006062
ID  - 23006062
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tesei, A
TI  - Local properties of solutions of a semilinear elliptic equation with an inverse-square potential
JF  - JOURNAL OF MATHEMATICAL SCIENCES (US)
J2  - J MATH SCI (US)
VL  - 149
PY  - 2008
IS  - 6
SP  - 1726
EP  - 1740
PG  - 15
SN  - 2372-5214
DO  - 10.1007/s10958-008-0092-2
UR  - https://m2.mtmt.hu/api/publication/23006066
ID  - 23006066
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Xiang, ZY
AU  - Mu, CL
AU  - Hu, XG
TI  - Support properties of solutions to a degenerate equation with absorption and variable density
JF  - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
J2  - NONLINEAR ANAL-THEOR
VL  - 68
PY  - 2008
IS  - 7
SP  - 1940
EP  - 1953
PG  - 14
SN  - 0362-546X
DO  - 10.1016/j.na.2007.01.021
UR  - https://m2.mtmt.hu/api/publication/23006061
ID  - 23006061
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Moschini, L
AU  - Tesei, A
TI  - Parabolic Harnack, inequality for the heat equation with inverse-square potential
JF  - FORUM MATHEMATICUM
J2  - FORUM MATH
VL  - 19
PY  - 2007
IS  - 3
SP  - 407
EP  - 427
PG  - 21
SN  - 0933-7741
DO  - 10.1515/FORUM.2007.017
UR  - https://m2.mtmt.hu/api/publication/23006063
ID  - 23006063
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Moschini, L
AU  - Reyes, G
AU  - Tesei, A
TI  - Nonuniqueness of solutions to semilinear parabolic equations with singular coefficients
JF  - COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
J2  - COMMUN PUR APPL ANAL
VL  - 5
PY  - 2006
IS  - 1
SP  - 155
EP  - 179
PG  - 25
SN  - 1534-0392
DO  - 10.3934/cpaa.2006.5.155
UR  - https://m2.mtmt.hu/api/publication/23006064
ID  - 23006064
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Pozio, MA
AU  - Tesei, A
TI  - On the uniqueness of bounded solutions to singular parabolic problems
JF  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES A
J2  - DISCRETE CONT DYN S
VL  - 13
PY  - 2005
IS  - 1
SP  - 117
EP  - 137
PG  - 21
SN  - 1078-0947
UR  - https://m2.mtmt.hu/api/publication/25497271
ID  - 25497271
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Reyes, G
AU  - Tesei, A
TI  - Self-similar solutions of a semilinear parabolic equation with inverse-square potential
JF  - JOURNAL OF DIFFERENTIAL EQUATIONS
J2  - J DIFFER EQUATIONS
VL  - 219
PY  - 2005
IS  - 1
SP  - 40
EP  - 77
PG  - 38
SN  - 0022-0396
DO  - 10.1016/j.jde.2005.06.031
UR  - https://m2.mtmt.hu/api/publication/23006065
ID  - 23006065
LA  - English
DB  - MTMT
ER  -