논문KCI 등재
Existence and Behavior Results for a Nonlocal Nonlinear Parabolic Equation with Variable Exponent
경북대학교 자연과학대학 수학과|2020.03|Kyungpook Mathematical Journal|제60권 제1호|pp. 145-161|DOI 10.5666/KMJ.2020.60.1.145
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In this article, we study the solvability of the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations with nonstandard growth and nonlocal terms. We prove the existence of weak solutions of the considered problem under more general conditions. In addition, we investigate the behavior of the solution when the problem is homogeneous.
Abstract
In this article, we study the solvability of the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations with nonstandard growth and nonlocal terms. We prove the existence of weak solutions of the considered problem under more general conditions. In addition, we investigate the behavior of the solution when the problem is homogeneous.
참고문헌 (35)
- R. A. Adams, "Sobolev spaces" (1975), Academic Press
- N. V. Afanas’eva, "Theorems on the existence and nonexistence of solutions to the Cauchy problem for degenerate parabolic equations with a nonlocal source", Ukrain. Mat. Zh, 57(11), pp.1443~1464 (2005)
- Y. Alkhutov, "Parabolic equations with variable order of nonlinearity", Collection of works of Institute of Mathematics NAS of Ukraine, 6, pp.23~50 (2009)
- J. R. Anderson, "Global existence for degenerate parabolic equations with a non-local forcing", Math. Methods Appl. Sci, 20, pp.1069~1087 (1997)
- S. N. Antontsev, "A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions", Nonlinear Anal., 60, pp.515~545 (2005)
- S. N. Antontsev, "Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity", J. Math. Sci, 150(5), pp.2289~2301 (2008)
- J. Bebernes, "Thermal behaviour for a confined reactive gas", J. Diff. Equations, 44, pp.118~133 (1992)
- J. Bebernes, "Mathematical problems from combustion theory" (1989), Springer
- M. Chipot, "On the asymptotic behavior of some nonlocal problems", Positivity, 3, pp.65~81 (1999)
- M. Chipot, "Existence and uniqueness results for a class of nonlocal elliptic and parabolic problems", Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal, 8(1), pp.35~51 (2001)
- M. Chipot, "Remarks on a nonlocal problem involving the Dirichlet energy", Rend. Sem. Mat. Univ. Padova, 110, pp.199~220 (2003)
- W. B. Deng, "The blow-up rate for a degenerate parabolic equation with a non-local source", J. Math. Anal. Appl, 264, pp.577~597 (2001)
- K. Deng, "The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers’ equation", Quart. Appl. Math, 50, pp.173~200 (1992)
- L. Diening, "Lebesgue and Sobolev spaces with variable exponents" (2017), Springer
- Yu. A. Dubinskii, "Weak convergence for nonlinear elliptic and parabolic equations", (Russian)Mat. Sb. (N. S. ), 67(109), pp.609~642 (1965)
- F. G. Duzgun, "Existence, uniqueness and behaviour of solutions for a nonlinear diffusion equation with third type boundary value condition", Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 26(4), pp.445~463 (2015)
- J. Furter, "Local vs. nonlocal interactions in population dynamics", J. Math. Biol, 27, pp.65~80 (1989)
- V. A. Galaktionov, "A general approach to critical Fujita exponents in nonlinear parabolic problems", Nonlinear Anal, 34, pp.1005~1027 (1998)
- A. S. Kalashnikov, "Some problems of qualitative theory of nonlinear degenerate secondorder parabolic equations", Russian Math. Surveys, 42, pp.169~222 (1987)
- O. Kovacik, "On spaces L p(x)and Wk,p(x)", Czechoslovak Math. J, 41, pp.592~618 (1991)
- O. A. Ladyzenskaya, "Linear and quasilinear equations of parabolic type" (1969), Mathematical Monographs
- J. L. Lions, "Quelques methodes de resolution des problemes aux limites non lineaires" (1969), Gauthier-Villars
- C. V. Pao, "Nonlinear parabolic and elliptic equations" (1992), Plenum Press
- C. V. Pao, "Blowing-up of solution for a nonlocal reaction-diffusion problem in combustion theory", J. Math. Anal. Appl, 166(2), pp.591~600 (1992)
- V. Radulescu, "Partial differential equations with variable exponents:variational methods and quantitative analysis" (2015), CRC Press, Taylor & Francis Group
- M. M. Rao, "Measure theory and integration" (1987), John Wiley & Sons
- P. Rouchon, "Universial bounds for global solutions of a diffusion equation with a nonlocal reaction term", J. Differential Equations, 193, pp.75~94 (2003)
- U. Sert, "On solvability of a class of nonlinear elliptic type equation with variable exponent", J. Appl. Anal. Comput, 7(3), pp.1139~1160 (2017)
- Ugur Sert, "Solvability of nonlinear elliptic type equation with two unrelated non standard growths", 대한수학회지, 55(6), pp.1337~1358 (2018), 대한수학회
- K. N. Soltanov, "Some embedding theorems and their applications to nonlinear equations", Differensial’nie Uravnenia, 20(12), pp.2181~2184 (1984)
- K. N. Soltanov, "On some modification Navier-Stokes equations", Nonlinear Anal, 52(3), pp.769~793 (2003)
- K. N. Soltanov, "Some nonlinear equations of the nonstable filtration type and embedding theorems", Nonlinear Anal, 65, pp.2103~2134 (2006)
- K. N. Soltanov, "Nonlinear equations in non-reflexive Banach spaces and strongly nonlinear differential equations", Adv. Math. Sci. Appl, 9(2), pp.939~972 (1999)
- P. Souplet, "Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source", J. Differential Equations, 153, pp.374~406 (1999)
- M. X. Wang, "Blow-up properties of positive solutions for nonlocal reaction diffusion problems", Math. Methods Appl. Sci, 19, pp.1141~1156 (1996)
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