THE CAUCHY PROBLEM FOR A DENGERATE PARABOLIC EQUATION WITH ABSORPTION

  • Lee, Jin-Ho (Department of mathematics Sookmyung Women's University)
  • Published : 2000.05.01

Abstract

The Cauchy problem for degenerate parabolic equations with absorption is studied. We prove the existence of a fundamental solution. Also a Harnack type inequality is established and the existence and uniqueness of initial trace for nonnegative solutions is shown.

Keywords

initial trace;degenerate pafabolic equation;absorption;Harnack inequality

References

  1. Trans. Amer. Math. Soc. v.307 no.2 A very singular solution of a quasilinear degenerate diffusion equation with absorption L.A. Peletier;J. Wang
  2. Revista. Math. Iber v.2 Non-negative solutions of generalized porous medium equation B.E.J. Dahlberg;C.E. Kenig
  3. Duke. Math. J. v.58 Classification of singular solutions of a nonlinear heat equation S. Kamin;L.A. Peletier;J.L. Vazquez
  4. J. Math. Pures Appl. v.62 Nonlinear parabolic equations involving measures as initial conditions H. Brezis;A. Friedman
  5. Nonnegative weak solutions of a porous medium equation with strong absorption C.K. Cho
  6. Arch. Rational Mech. Anal. v.100 Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations E. DiBenedetto
  7. Kangweon-kyungki Math. J. v.5 Uniqueness of solutions for a degenerate parabolic equation with absorption J.H. Lee
  8. Arch. Rational Mech. Anal. v.75 A very singular solution of the heat equation with absorption H. Brezis;L.A. Peletier;D. Terman
  9. Nonlinear Analysis Theory, Methods and Applications v.18 Holder continuity for solutions of certain degenerate parabolic systems H.J. Choe
  10. Hokkido. Math. J. v.27 Cauchy problem of momlinear parabolic equations with bounded measurable coefficients H.J. Choe;J.H. Lee
  11. J. Diff. Eq. v.102 The asymptotic behavior of solutions of a quasi linear degenerate parabolic equation Z. Junning
  12. Trans. Amer. Math. Soc. v.314 On the Cuachy problem and initial traces for a degenerate parabolic equation E. DiBenedetto;M.A Herrero
  13. J. Rreine Angew. Math. v.357 Holder estimated for nonlinear degenerate parabolic systems E. DiBenedetto;A. Friedman