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On the uniqueness of bounded solutions to singular parabolic problems
1. | Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", P.le A. Moro 5, I-00185 Roma, Italy, Italy |
[1] |
Maria Assunta Pozio, Fabio Punzo, Alberto Tesei. Uniqueness and nonuniqueness of solutions to parabolic problems with singular coefficients. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 891-916. doi: 10.3934/dcds.2011.30.891 |
[2] |
Luisa Moschini, Guillermo Reyes, Alberto Tesei. Nonuniqueness of solutions to semilinear parabolic equations with singular coefficients. Communications on Pure and Applied Analysis, 2006, 5 (1) : 155-179. doi: 10.3934/cpaa.2006.5.155 |
[3] |
Constantin Christof, Dominik Hafemeyer. On the nonuniqueness and instability of solutions of tracking-type optimal control problems. Mathematical Control and Related Fields, 2022, 12 (2) : 421-431. doi: 10.3934/mcrf.2021028 |
[4] |
C. García Vázquez, Francisco Ortegón Gallego. On certain nonlinear parabolic equations with singular diffusion and data in $L^1$. Communications on Pure and Applied Analysis, 2005, 4 (3) : 589-612. doi: 10.3934/cpaa.2005.4.589 |
[5] |
Hyungjin Huh. Self-similar solutions to nonlinear Dirac equations and an application to nonuniqueness. Evolution Equations and Control Theory, 2018, 7 (1) : 53-60. doi: 10.3934/eect.2018003 |
[6] |
Stephen Pankavich, Petronela Radu. Nonlinear instability of solutions in parabolic and hyperbolic diffusion. Evolution Equations and Control Theory, 2013, 2 (2) : 403-422. doi: 10.3934/eect.2013.2.403 |
[7] |
Mark I. Vishik, Sergey Zelik. Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2059-2093. doi: 10.3934/cpaa.2014.13.2059 |
[8] |
Paulo Cesar Carrião, R. Demarque, Olímpio H. Miyagaki. Nonlinear Biharmonic Problems with Singular Potentials. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2141-2154. doi: 10.3934/cpaa.2014.13.2141 |
[9] |
Ida De Bonis, Daniela Giachetti. Singular parabolic problems with possibly changing sign data. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2047-2064. doi: 10.3934/dcdsb.2014.19.2047 |
[10] |
Laurence Cherfils, Stefania Gatti, Alain Miranville. A doubly nonlinear parabolic equation with a singular potential. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 51-66. doi: 10.3934/dcdss.2011.4.51 |
[11] |
Gary Lieberman. A new regularity estimate for solutions of singular parabolic equations. Conference Publications, 2005, 2005 (Special) : 605-610. doi: 10.3934/proc.2005.2005.605 |
[12] |
Shota Sato, Eiji Yanagida. Asymptotic behavior of singular solutions for a semilinear parabolic equation. Discrete and Continuous Dynamical Systems, 2012, 32 (11) : 4027-4043. doi: 10.3934/dcds.2012.32.4027 |
[13] |
Sabri Bensid, Jesús Ildefonso Díaz. Stability results for discontinuous nonlinear elliptic and parabolic problems with a S-shaped bifurcation branch of stationary solutions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1757-1778. doi: 10.3934/dcdsb.2017105 |
[14] |
Kin Ming Hui, Sunghoon Kim. Existence of Neumann and singular solutions of the fast diffusion equation. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 4859-4887. doi: 10.3934/dcds.2015.35.4859 |
[15] |
Alexandre Nolasco de Carvalho, Marcos Roberto Teixeira Primo. Spatial homogeneity in parabolic problems with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2004, 3 (4) : 637-651. doi: 10.3934/cpaa.2004.3.637 |
[16] |
Luis Alvarez, Jesús Ildefonso Díaz. On the retention of the interfaces in some elliptic and parabolic nonlinear problems. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 1-17. doi: 10.3934/dcds.2009.25.1 |
[17] |
M. Delgado-Téllez, Alberto Ibort. On the geometry and topology of singular optimal control problems and their solutions. Conference Publications, 2003, 2003 (Special) : 223-233. doi: 10.3934/proc.2003.2003.223 |
[18] |
Andrzej Szulkin, Shoyeb Waliullah. Infinitely many solutions for some singular elliptic problems. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 321-333. doi: 10.3934/dcds.2013.33.321 |
[19] |
Simona Fornaro, Maria Sosio, Vincenzo Vespri. Harnack type inequalities for some doubly nonlinear singular parabolic equations. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5909-5926. doi: 10.3934/dcds.2015.35.5909 |
[20] |
Hirotoshi Kuroda, Noriaki Yamazaki. Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations. Conference Publications, 2009, 2009 (Special) : 486-495. doi: 10.3934/proc.2009.2009.486 |
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