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2015 | 13 | 1 |
Tytuł artykułu

A new kind of the solution of degenerate parabolic equation with unbounded convection term

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-03-20
zaakceptowano
2014-08-26
online
2015-05-05
Twórcy
autor
  • School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, Fujian
    Province, P.R. China
Bibliografia
  • [1] Anzellotti G. and Giaquinta M., Funzioni BV e trace. Rend. Sem. Math. Padova, 1978, 60, 1-21
  • [2] Baccardo L., Orsina L. and Porretta A., Some noncoercive parabolic equations with lower order terms, J. Evol.Equ., 2003, 3, 407-418
  • [3] Bendanamane M. and Karlsen K. H., Reharmonized entropy solutions for quasilinear anisotropic degenerate parabolic equations,SLAM J. Math. Annal., 2004, 36(2), 405-422
  • [4] Bénilan Ph., Crandall M. G. and Pierre M., Solutions of the porous medium equation under optimal conditions on initial values,Indiana Univ. Math. J., 1984, 33, 51-87
  • [5] Brezis H. and Crandall M. G., Uniqueness of solutions of the initial value problem for ut Δ φ (u) = 0, J. Math.Pures et Appl., 1979, 58, 564-587
  • [6] Carrillo J., Entropy solutions for nonlinear degenerate problems, Arch. Rational Mech. Anal.,1999, 147, 269-361
  • [7] Chen G.Q. and Karlsen K.H., Quasilinear anisotropic degenerate parabolic equations with time-space degenerate diffusioncoefficients, Comm. Pure. Appl. Anal., 2005, 4(2), 2005, 241-267[Crossref]
  • [8] Chen G.Q. and Perthame B., Well-Posedness for non-isotropic degenerate parabolic-hyperbolic equations, Ann. I. H. Poincare-AN, 2003, 20(4), 645-668[Crossref]
  • [9] Cockburn B. and Gripenberg G. , Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations,J. Diff. Equations,1999,151, 231-251
  • [10] Deck T. and Ruse S. K., Parabolic differential equations with unbounded coefficients-a generalization of the parametric method,Acta Appl. Math., 2002, 74, 71-91
  • [11] Evans L.C., Weak convergence methods for nonlinear partial differential equations, Conference Board of the MathematicalSciences, Regional Conferences Series in Mathematics, 74, American Mathematical Society, 1998, 1-66
  • [12] Fabrie P. and Gallouet T. , Modeling wells in porous media flows, Math. Models Methods Appl. Sci., 2000, 10, 673-709
  • [13] Ishige K. and Murata M. , An intrinsic metric approach to uniqueness of the positive Cauchy problem for parabolic equations,Math. Z., 1998, 227, 313-335
  • [14] Karlsen K. H. and Ohlberger M., A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations, J. ofMath. Ann. Appl., 2002, 275, 439-458
  • [15] Kružkov N., First order quasilinear equations in several independent variables, Math. USSR-Sb., 1970, 10, 217-243
  • [16] Pinchover Y., On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unboundedcoefficients, Math. Z., 1996, 223, 569-586
  • [17] Vol0pert A.I., BV space and quasilinear equations, Mat. Sb., 1967, 73, 255-302
  • [18] Vol0pert A.I. and Hudjaev S.I. , Cauchy’s problem for degenerate second order quasilinear parabolic equations, Mat. Sbornik,1969, 78(120), 374-396; Engl. Transl.: Math.USSR Sb., 1969, 7(3), 365-387
  • [19] Vol0pert A.I. and Hudjaeve S.I., Analysis of class of discontinuous functions and the equations of mathematical physics, Izda.Nauka Moskwa, 1975 (in Russian)
  • [20] Wu Zh. and Yin J., Some properties of functions in BVx and their applications to the uniqueness of solutions for degeneratequasilinear parabolic equations, Northeastern Math. J., 1989, 5(4), 395-422
  • [21] Wu Z. and Zhao J., The first boundary value problem for quasilinear degenerate parabolic equations of second order in severalvariables, Chin. Ann. of Math., 1983, 4B(3), 319-358
  • [22] Wu Z., Zhao J., Yin J. and li H., Nonlinear Diffusion Equations, Word Scientific Publishing, Singapore, 2001.
  • [23] Zhan H. and Zhao J., The stability of solutions for second order quasilinear degenerate parabolic equations, Acta Math. Sinica,2007, 50, 615-628 (in chinese)
  • [24] Zhao J., Uniqueness of solutions of quasilinear degenerate parabolic equations, Northeastern Math. J., 1985, 1(2), 153-165
  • [25] Zhao J. and Zhan H., Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations,Science in China Ser. A, 2005, 48, 583-593
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0029
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