DOI QR코드

DOI QR Code

HYPERBOLIC EQUATIONS RELATED TO p-LAPLACIAN OPERATORS VIA TIME DISCRETIZATION METHODS

  • Shin, Kiyeon (Department of Mathematics, Pusan National University) ;
  • Kang, Sujin (Department of Nanomaterials Engineering, Pusan National University)
  • 투고 : 2014.04.14
  • 심사 : 2014.08.01
  • 발행 : 2014.09.30

초록

In this paper we consider hyperbolic equations related to the p-Laplacian with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

키워드

과제정보

연구 과제 주관 기관 : Pusan National University

참고문헌

  1. Adams, R., Sobolev Spaces, Academic Press, New York, 1975.
  2. Barbu, V., Nonlinear semigroups and differential equations in Banach spaces, Noordho Internat. Publ., Leyden, 1976.
  3. Bensoussan, A., Boccardo, L., Murat, F., On a nonlinear P.D.E. having natural growth terms and unbounded solutions, Ann. Inst. H. Poincare 5 (1988), no.4, 347-364.
  4. Brezis, H., Semi-groups non lineaires et applications, Sympos. Math. 7, Academic Press, London, 1971.
  5. Le, V., Schmit, K., Global Bifurcation in Variational Inequalities, Springer-Verlag, New York, 1997.
  6. Lions, J.L., Quelques methodes de resolution des problemes aux limites non lieaires, Dunod Gauthier-Villars, Paris, 1969.
  7. Lions, J.L., Strauss, W.A., Some non-linear evolution equations, Bull. Soc. Math. France, 9 (1965), 43-96.
  8. J.M. Rakotoson, On some degenerate and nondegenerate Quasilinear Elliptic systems with nonhomogeneous Dirichlet boundary condition, Nonlinear Analysis, T.M.A., 13 (1989), no.2, 165-183. https://doi.org/10.1016/0362-546X(89)90042-4
  9. R.E. Showalter, Monotone operators in Banach space and nonlinear partial di erential equations, Mathematical Surveys and Monographs 49, AMS, 1996.