Kalashnikov AS: Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations. Russian Mathematical Surveys 1987,42(2):169–222. 10.1070/RM1987v042n02ABEH001309
Article
MATH
MathSciNet
Google Scholar
Abdulla UG: On the Dirichlet problem for the nonlinear diffusion equation in non-smooth domains. Journal of Mathematical Analysis and Applications 2001,260(2):384–403. 10.1006/jmaa.2001.7458
Article
MATH
MathSciNet
Google Scholar
Abdulla UG: Well-posedness of the Dirichlet problem for the non-linear diffusion equation in non-smooth domains. Transactions of the American Mathematical Society 2005,357(1):247–265. 10.1090/S0002-9947-04-03464-6
Article
MATH
MathSciNet
Google Scholar
DiBenedetto E: Continuity of weak solutions to certain singular parabolic equations. Annali di Matematica Pura ed Applicata. Serie Quarta 1982,130(1):131–176. 10.1007/BF01761493
Article
MATH
MathSciNet
Google Scholar
DiBenedetto E: Continuity of weak solutions to a general porous medium equation. Indiana University Mathematics Journal 1983,32(1):83–118. 10.1512/iumj.1983.32.32008
Article
MATH
MathSciNet
Google Scholar
Ziemer WP: Interior and boundary continuity of weak solutions of degenerate parabolic equations. Transactions of the American Mathematical Society 1982,271(2):733–748. 10.1090/S0002-9947-1982-0654859-7
Article
MATH
MathSciNet
Google Scholar
Abdulla UG: On the Dirichlet problem for reaction-diffusion equations in non-smooth domains. Nonlinear Analysis 2001,47(2):765–776. 10.1016/S0362-546X(01)00221-8
Article
MATH
MathSciNet
Google Scholar
Abdulla UG: First boundary value problem for the diffusion equation. I. Iterated logarithm test for the boundary regularity and solvability. SIAM Journal on Mathematical Analysis 2003,34(6):1422–1434. 10.1137/S0036141002415049
Article
MATH
MathSciNet
Google Scholar
Abdulla UG: Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation. Boundary Value Problems 2005,2005(2):181–199. 10.1155/BVP.2005.181
Article
MATH
MathSciNet
Google Scholar
Petrovsky IG: Zur ersten Randwertaufgabe der Wärmeleitungsgleichung. Compositio Mathematica 1935, 1: 383–419.
MathSciNet
Google Scholar
Abdulla UG: Reaction-diffusion in a closed domain formed by irregular curves. Journal of Mathematical Analysis and Applications 2000,246(2):480–492. 10.1006/jmaa.2000.6800
Article
MATH
MathSciNet
Google Scholar
Abdulla UG: Reaction-diffusion in irregular domains. Journal of Differential Equations 2000,164(2):321–354. 10.1006/jdeq.2000.3761
Article
MATH
MathSciNet
Google Scholar
Abdulla UG: Evolution of interfaces and explicit asymptotics at infinity for the fast diffusion equation with absorption. Nonlinear Analysis 2002,50(4):541–560. 10.1016/S0362-546X(01)00764-7
Article
MATH
MathSciNet
Google Scholar
Abdulla UG, King JR: Interface development and local solutions to reaction-diffusion equations. SIAM Journal on Mathematical Analysis 2000,32(2):235–260. 10.1137/S003614109732986X
Article
MATH
MathSciNet
Google Scholar
Wiener N: The Dirichlet problem. Journal of Mathematics and Physics 1924, 3: 127–146.
MATH
Google Scholar
Feireisl E, Petzeltová H, Simondon F: Admissible solutions for a class of nonlinear parabolic problems with non-negative data. Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2001,131(4):857–883. 10.1017/S0308210500001153
Article
MATH
MathSciNet
Google Scholar
Friedman A: Partial Differential Equations of Parabolic Type. Prentice-Hall, New Jersey; 1964:xiv+347.
MATH
Google Scholar
Ladyzhenskaya OA, Solonnikov VA, Uralceva NN: Linear and Quasilinear Equations of Parabolic Type. American Mathematical Society, Rhode Island; 1968.
Google Scholar
Lieberman GM: Second Order Parabolic Differential Equations. World Scientific, New Jersey; 1996:xii+439.
Book
MATH
Google Scholar