Department of Mathematics

Qi Zhang Publications

Technical Publications

Journal Articles

1. Zhang, Q. 1993. On a complex equation arizing on Hele-Shaw flow. Applied Mathematics Letters. p.45-47. (Refereed)  

2. Zhang, Q. 1995. A Hanarck inequality for Kolmogorov equations. J.Math Analysis and Applications. p.402-418. (Refereed) 

3. Zhang, Q. 1996. On a parabolic equation with a singular lower order term Part II: The Gaussian Bounds. Indiana University Math. Journal. p.989-1020. (Refereed)  

4. Zhang, Q. 1996. On aparabolic equation with a singular lower order term. Transactions AMS. p.2867-2899. (Refereed)  

5. Zhang, Q. 1996. A Hanarck inequality for the equation Δ(aΔu)+bΔu=0 when ¦b¦ ε Kn+1. Manuscripta Mathematica. p.61-78. (Refereed)  

6. Zhang, Q. 1996. A Hanarck inequality for Kolmogorov equations. J.Math Analysis and Applications. p.402-418. (Refereed)  

7. Zhang, Q. 1997. Nonlinear parabolic problems on manifolds and nonexistence result of the non-compoact Yamabe problem. Elect. Research Announcement AMS. p.45-51. (Refereed)  

8. Zhang, Q. 1997. Global Existence and local continuity of solutions for semilinear paprabolic equations. COMM PDE. p.1529-1557. (Refereed)  

9. Zhang, Q. 1997. Gaussian Bounds for the fundamental Solutions of Δ(aΔu)+bΔu-ut=0. Manuscripta Math. p.381-391. (Refereed)  

10. Zhang, Q., Zhao, Z. 1998. Global asymptotic behavior of solutions for a semilinear parabolic equations. Proceedings AMS. p.1491-1500. (Refereed)  

11. Zhang, Q. 1998. Blow up and global existence of solutions to an inhomogeneous parabolic system. J.Diff. Equations. Vol. 147: p.155-183. (Refereed)  

12. Zhang, Q., Zhao, Z. 1998. Singular Solutions of semilinear elliptic and parabolic equations. Math. Annalen. p.777-794. (Refereed)  

13. Zhang, Q. 1998. The critical exponent for a reaction diffusion equation on some Lie groups. Math. Zeit. p.51-72. (Refereed)  

14. Zhang, Q. 1998. A new critical phenonmenon for semilinear parabolic problems. J. Math. Analysis and Applications. p.125-139. (Refereed)  

15. Zhang, Q. 1999. Blow up results for nonlinear parabolic equations on manifolds. Duke Math J. Vol. 97: p.515-540. (Refereed)  

16. Zhang, Q. 1999. A priori estimates and the representation formula for all positive solutions to a semilinear parabolic problem. J.Math. Analysis and Applications. p.413-427. (Refereed)  

17. Zhang, Q., Bandle, C., Levine, H.A. 2000. Critical exponents of fujita type for in homogeneoeus parabolic equations and systems. J, Math Analysis and Appl. p.624-648. (Refereed)  

18. Zhang, Q. 2000. An optimal parabolic estimate and it's applocations in prescribing scalar curvature on open manifolds with Ricci ≥0. Math. Ann. p.703-731. (Refereed)  

19. Zhang, Q., Levine, H.A. 2000. The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values. Proc. Royal Soc. Edin. p.591-602. (Refereed)  

20. Zhang, Q. 2000. A new critical behavior for nonlinear wave equations. J. Computational Analysis and Applications. Vol. 2: 4 p.277-292. (Refereed)  

21. Zhang, Q. 2000. Semilinear parabolic problems on manifolds and applications to the non-compact Yamabe problem. Electron. J. Diff. Equations. p.1-30. (Refereed)  

22. Zhang, Q., Zhao, Z. 2000. Existence results on prescribing zero scalar curvature. Diff. And Int. Equations. p.779-790. (Refereed)  

23. Zhang, Q., Zhao, Z. 2000. Estimate of global bounds for some Schrödinger heat kernels on manifolds. Illinois J. Math. p.556-573. (Refereed)  

24. Zhang, Q., Souplet, P. 2001. A blow up result for a nonlinear wave equation with damping: the critical case. C.R. Acad. Sci. Paris. Vol. 333: 2 p.109-114. (Refereed)  

25. Zhang, Q., Goldstein, J.A. 2001. On a degenerate heat equation with a singular potential. J.Functional Analysis. Vol. 186: 2 p.342-359. (Refereed)  

26. Zhang, Q. 2001. A liouville type theorem for some critical semilinear elliptic equations on noncomponent manifolds. Indiana U. Math. Vol. 50: 4 p.1915-1936. (Refereed)  

27. Zhang, Q. 2001. Global bounds of Schrödinger heat kernels with negative potentials. J. Functional Analysis. Vol. 182: 2 p.342-359. (Refereed)  

28. Zhang, Q. 2001. The quantizing effect of potentials on the critical number of reaction diffusion equations. J. Diff. Equations. Vol. 170: p.188-314. (Refereed)  

29. Zhang, Q. 2001. Global lower bound for the heat kernel of -Δ+¦ae¦2. Proceedings AMS. Vol. 170: p.1105-1112. (Refereed)  

30. Zhang, Q., Souplet, P. 2001. Existence of ground states for semilinear elliptic equations with decaying mass: a parabolic approach. C.R. Acad. Sci. Paris. p.515-520. (Refereed)  

31. Zhang, Q. 2001. A general blowup result on nonlinear boundary value problems on exterior domains. Proceedings R.S. Edinburg. p.451-475. (Refereed)  

32. Zhang, Q. 2001. Large time behavior of Schrödinger heat kernels and applications. Comm. Math. Physics. p.1105-1112. (Refereed)  

33. Zhang, Q. 2002. A critical behavior form some semilinear parabolic equations involving sign changing solutions. Nonlinear Analysis. Vol. 50: p.967-980. (Refereed)  

34. Zhang, Q., Souplet, P. 2002. Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states. Annales Inst. H. Poincare, Nonlineaire. Vol. 19: 5 p.683-703. (Refereed)  

35. Zhang, Q. 2003. Finite energy solutions to the Yamabe equation. Geom. Dedicata. p.153-165. (Refereed)  

36. Zhang, Q. 2003. The global behavior of head kernels in exterior domains. Journal of Functional Analysis. Vol. 200: 1 p.160-176. (Refereed)  

37. Zhang, Q. 2003. Global solutions of Navier-stokes equations in a new function space. Asian Journal of Mathematics. p.337=364. (Refereed)  

38. Zhang, Q. 2003. A sharp comparison result concerning Schrödinger heat kernels. Bulletin London Math. Socitey. Vol. 35: 4 p.461-472. (Refereed)  

39. Zhang, Q. 2003. The boundary behavior of heat kernels of Dirichlet Laplacians. Journal of Differential equations. Vol. 182: 2 p.416-430. (Refereed)  

40. Zhang, Q. 2003. A Kazdan-Warner Type condition and heat kernels estimates on noncompact manifolds. Indiana, U. Math. J. p.1075-1111. (Refereed)  

41. Zhang, Q., Wong, B. 2003. Refined gradient bounds, poisson equations and some applications to open Kähler manifolds. Asian Journal of Mathematics. Vol. 7: 3 p.337-364. (Refereed)  

 42. Zhang, Q., Goldstein, J.A. 2003. Linear parabolic equations with strong singular potentials. Transactions AMS. Vol. 355: 1 p.197-211. (Refereed)  

43. Zhang, Q., Liskevich, V. 2004. Positive solutions to Δu-Vu+Wup=0 and its parabolic counterpart in noncompact manifolds. Pacific Journal of Math. p.163-200. (Refereed)  

44. Zhang, Q., Liskevich, V. 2004. Extra regularity result for parabolic equations with drift. Manuscripta Math. p.191-209. (Refereed)  

45. Zhang, Q. 2004. A strong regularity result for parabolic equations. Comm. Math. Physics. p.245-260. (Refereed)  

46. Zhang, Q., Yordanov, B. 2005. Finite time blow up for wave equations with a potential. SUAN journal of mathematical analysis. p.1426-1433. (Refereed)  

47. Grujic, Z., Zhang, Q. 2006. Space-Time Localization of a Class of Geometric Criteria for Preventing Blow-up in the 3D NSE. Commun. Math. Phys. p.555-564. (Refereed)  

48. Yordanov, B., Zhang, Q. 2006. Finite time blow up for critical wave equations in high dimensions. Journal of Functional Analysis. p.361-374. (Refereed)  

49. Zhang, Q. 2006. Some Gradient Estimates for the Heat Equation on Domains and for an Equation by Perelman. International Mathematics Research Notices. p.1-39. (Refereed)  

50. Souplet, P., Zhang, Q. 2006. Sharp Gradient Estimate and Yau's Liouville Theorem for the Heat Equation on Noncompact Manifolds. Bulletin London Math. Soc. p.1045-1053. (Refereed)  

51. Zhang, Q. 2006. Stability of the Cheng-Yau Gradient Estimate. Pacific Journal of Math. p.379-398. (Refereed)  

52. Souplet, P., Zhang, Q. 2006. Global Solutions of Inhomogeneous Hamilton-Jacobi Equations. Journal Analyse Math. p.355-396. (Refereed)  

53. Zhang, Q. 2006. Local Estimates on Two Linear Parabolic Equations with Singular Coefficients. Pacific Journal of Math. p.367-396. (Refereed)  

54. Zhang, Q. 2006. The ill posed Navier-Stokes equation in connected sum of R3. Complex Vairables and Elliptic Equations. p.1059-1063. (Refereed)  

55. Zhang, Q. 2007. A Uniform Sobolev Inequality Under Ricci Flow. International Mathematics Research Notices. 17p. (Refereed)  

(In Press)

1. Coulhon, T., Zhang, Q. Large Time Behavior of Heat Kernels on Forms. J. Differential Geometry. (Accepted 05/24/2006. 32 manuscript pages.) (Refereed)

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