Dr. C. V. Pao
Professor of Mathematics
Nonlinear Reaction-Diffusion Equations (09/09/07)
C.V.Pao, Eigenvalue problems of a degenerate quasilinear
elliptic equation, Rocky Mountain J. Math.,(to appear).
C.V.Pao, Global attractor of a competitor-competitor-mutualist
reaction-diffusion system with time delays, Nonlinear Analysis,
(to appear).
C.V.Pao, Numerical methods for qusilinear elliptic
equations with nonlinear boundary conditions, SIAM J.Numer. Anal.,
45(2007),1081-1106.
C.V. Pao and W.H.Ruan, Positive solutions of quasilinear
parabolic systems with nonlinear boundary conditions, J. Math.
Anal. Appl., 333(2007) 472-499.
C.V.Pao, Monotone iterative methods for numerical solutions
of nonlinear integro-elliptic boundary problems, Applied Math.
Comput.,186(2007),1624-1642.
M.Y.Wang and C.V. Pao, Time-delayed finite difference
reaction-diffusion systems with nonquasimonotone functions, Numer.
Math., 103(2006), 485-513.
C.V.Pao, Quasilinear parabolic and elliptic equations with
nonlinear boundary conditions, Nonlinear Analysis, 66(2006),639-662.
C.V.Pao, Strongly coupled elliptic systems and applications to
Lotka-Volterra models with cross-diffusion, Nonlinear Analysis, 60(2005),
1197-1217
C.V.Pao, Stability and attractivity of periodic solutions of
parabolic systems with time delays, J. Math. Anal. Appl., 304(2005),
423-450.
C.V.Pao Global asymptotic stability of Lotka-Volterra
competition systems with diffusion and time delays. Nonlinear Anal.
Real World Appl. 5 (2004), 91--104.
C.V.Pao Global attractor of a coupled finite difference
reaction diffusion system with delays, J. Math. Anal. Appl.
288(2003),
251-273.
C.V.Pao Global asymptotic stability of Lotka-Volterra
3-species
reaction-diffusion systems with time delays. J. Math. Anal. Appl.
281
(2003) 186--204.
C.V.Pao Accelerated monotone iterations for numerical
solutions of nonlinear elliptic boundary value problems, Computers
Math. Appl. 46(2003), 1535-1544.
C.V.Pao Finite difference reaction-diffusion systems with
coupled boundary conditions and time delays. J. Math. Anal. Appl.
272 (2002), 407--434.
C.V.Pao Periodic solutions for systems of time-delayed
paraboli
equations in $\Bbb R\sp n$. Int. J. Pure Appl. Math. 1
(2002),299--315.
C.V.Pao Time delayed parabolic systems with coupled
nonlinear
boundary conditions. Proc. Amer. Math. Soc. 130 (2002),
1079--1086
.
C.V.Pao Convergence of solutions of reaction-diffusion
systems
with time delays. Nonlinear Anal. 48 (2002), 349--362.
c.v Pao and S.S.Cheng Entire solutions of discrete
elliptic equations, Southeast Asian Bull. Math. 26(2002) 267-278.
C.V.Pao Reaction diffusion systems with time delays in a
half-space domain. Proceedings of the Third World Congress of Nonlinear
Analysts, Part 7 (Catania, 2000). Nonlinear Anal. 47 (2001),
4365--4375.
C.V.Pao Numerical methods for time-periodic solutions of
nonlinear parabolic boundary value problems. SIAM J. Numer. Anal.
39
(2001), 647--667.
C.V.Pao Numerical solutions of reaction-diffusion
equations
with nonlocal boundary conditions. J. Comput. Appl. Math. 136
(2001),
227--243.
C.V.Pao Finite difference solutions of reaction diffusion
equations with continuous time delays. Advances in difference
equations,
III. Comput. Math. Appl. 42 (2001), 399--412.
C.V.Pao Numerical methods for fourth-order nonlinear
elliptic
boundary value problems. Numer. Methods Partial Differential
Equations
17 (2001), 347--368.
C.V.Pao Numerical methods for nonlinear integro-parabolic
equations of Fredholm type. Comput. Math. Appl. 41 (2001),
857--877.
C.V.Pao Quenching problem of a functional parabolic
equation,
Advances in Quenching, Dyn. Contin. Discrete Impuls. Syst. Ser. A
Math.
Anal. 8 (2001), 89--98.
C.V.Pao System of reaction-diffusion equations in a half
-space domain, Commun. Appl. Anal. 5 (2001), 307--318.
C.V.Pao Periodic solutions of parabolic systems with time
delays. J. Math. Anal. Appl. 251 (2000), 251--263.
C.V.Pao Periodic solutions of system of parabolic
equations in
unbounded domains, Lakshmikantham's legacy: a tribute on his 75th
birthday. Nonlinear Anal. 40 (2000), 523--535.
J.H.Wang and C.V.Pao Finite difference
reaction-diffusion
equations with nonlinear diffusion coefficients, Numer. Math. 85
(2000),
485--502.
C.V.Pao On fourth-order elliptic boundary value problems,
Proc. Amer. Math. Soc. 128(2000), 1023-1030.
C.V.Pao Quenching problem of a reaction-diffusion
equation with
time delay, Nonlinear Analysis, 41 (2000), 133--142.
C.V.Pao Dynamics of a Volterra-Lotka competition model
with
diffusion and time delays, Integral and Integrodifferential
Equations,
SIMAA 2, Gordon-Breach, Amesterdam, 2000, pp 269-277.
C.V.Pao Numerical methods for systems of nonlinear
parabolic
equations with time delays, J. Math. Anal. Appl.,
240(1999),249-279.
C.V.Pao Periodic solutions of parabolic systems with
nonlinear
boundary conditions, J. Math. Anal. Appl., 234(1999), 695-716.
C.V.Pao Numerical analysis of coupled system of
nonlinear
parabolic equations, SIAM J. Numer. Anal.,36(1999), 393-416.
Z.P.Yang and C.V.Pao Positive solutions and dynamics of
some
reaction diffusion models in HIV transmission, Nonlinear Analysis,
TMA,
35(1999), 323-341.
C.V.Pao Parabolic systems in unbounded domains, II.
Equations
with time delay.
C.V.Pao Monotone iterations for numerical solutions of
reaction-diffusion equations with time delay, Numer. Methods
Parttial
Differential Eq. 14(1998), 339-351.
C.V.Pao Accelerated monotone iterative methods for
finite
difference equations of reaction-diffution, Numer. Math. 79(1998),
261-281.
C.V.Pao Monotone Methods for a finite Difference System
of
Reaction Diffusion Equation with Time Delay, in "Advances in
Diffusion
Equations II", J. Compu. Math. Appl. 36(1998) 37-47.
C.V.Pao Dynamics of a Finite Difference System of
Reaction
Diffusion Equations with Time Delay, J. Difference Equations
Appl.,
4(1998), 1-11.
C.V.Pao Asymptotic behavior of solutions of
reaction-diffusion
equations with nonlocal boundary conditions, J. Comput. Appl. Math.
88(1998), 225-238.
C.V.Pao Parabolic systems in unbounded domains. I.
Existence $
dynamics. J. Math. Anal. Appl., 217(1998),129-160
C.V.Pao Dynamics of reaction-diffusion systems and
applicatio$
Nonlinear Analysis, TMA, 30(1997) 3371-3377
C.V.Pao Dynamics of weakly coupled parabolic systems
with
nonlocal boundary conditions, in " Advances in Nonlinear Dynamics":
Stability and Control, vol. 5, 1997, 319-327
C.V.Pao System of Parabolic Equations with Continuous
and
Discrete Delays, J. Math. Anal. Appl., 205(1997), 157-185
C.V.Pao Blowing-up and asymptotic behavior of solutions
for a
finite difference system, J. Applicable Analysis, 62(1996),
29-38
C.V.Pao Quasisolutions and Global Attractor of Reaction
Diffusion Systems, Nonlinear Analysis: TMA, 26(1996),
1889--1903
C.V.Pao Dynamics of Nonlinear Parabolic Systems with
Time Del$
J. Math. Anal. Appl., 198(1996), 751--779
S.Carl, Ch. Grossmann and C.V.Pao
Existence a$
Monotone Iterations for Parabolic Differential Inclusions, Comm.
Appl.
Nonlin. Anal., 3(1996), 1--24
C.V.Pao Block Monotone Iterative Methods for Numerical
Soluti$
Nonlinear elliptic Equations, Numer. Math., 72(1995),
239--262
C.V.Pao Coupled Nonlinear Parabolic Systems with Time
Delays,
J. Math. Anal. Appl., 196(1995), 237--265
C.V.Pao Reaction Diffusion Equations with Nonlocal
Boundary a$
Nonlocal Initial Conditions, J. Math. Anal. Appl., 195(1995),
702--718
C.V.Pao Finite Difference Reaction Diffusion Equations
with
Nonliner Boundary Conditions, Numer. Meth. Part. Diff. Eqs.,
11(1995),
355--374
W.H.Ruan and C.V.Pao Positive Steady-state
Solutions o$
Competing Reaction Diffusion System, J. Differential Equations,
117(1995), 411--427
C.V.Pao Dynamics of a Reaction Diffusion System Arising
from
Ecology, Nonlinear times and Digest, 2(1995), 47--57
C.V.Pao Dynamics of Reaction Diffusion Equations with
Nonlocal
Boundary Conditions, Quart. Appl. Math., 53(1995), 173--186
C.V.Pao Comparison Methods and Stability Analysis of
Reaction
Diffusion Systems, ``Comparison Methods and Stability Theory''(Ed.
by
X.~Liu and D.~Siegel), Marcel Dekker, New York, Lecture Notes in Pure and
Appl.
Math., V162, 277--292, 1994
C.V.Pao Nonlinear Elliptic Systems in Unbounded Domains,
Nonlin. Anal.: TMA, 22(1994), 1391--1407
C.V.Pao Positive Solutions and Dynamics of a Finite
Differenc Reaction Diffusion System, Numer. Meth. Part. Diff. Eqs.,
9(1993), 285--311
W.H.Ruan and C.V.Pao Asymptotic Behavior and
Positive Solutions of a Chemical Reaction Diffusion System, J. Math.
Anal. Appl., 169(1992), 157--178
C.V.Pao Nonlinear Elliptic Boundary Value Problems in Unbounded
Domains, J. Nonlin. Anal.: TMA, 18(1992), 759--774
C.V.Pao Blowing-up of Solution for a Nonlocal
Reaction-diffusion Problem in Combustion Theory, J. Math. Anal. Appl.,
166(1992),591--600
C.V.Pao Convergence of Coupled Systems of Nonlinear Finite
Difference elliptic equations, Diff. Integral Eqs., 3(1990), 381--396
C.V.Pao Numerical Methods for Coupled Systems of Nonlinear
Parabolic Boundary Value Problems, J. Math. Anal. Appl., 151(1990),
581--608
C.V.Pao Asymptotic Behavior of Solutions for Finite Difference
Equations of Reaction Diffusion, J. Math. Anal. Appl., 144(1989),
206--225
C.V.Pao Numerical Methods for Some Coupled Nonlinear Boundary
Value Problems, Diffusion Equations and Applications(ed. by
A.~R.~Astabizadeh, Ed.) Ohio University Press, 1988, 164--169
C.V.Pao Asymptotic Behavior of Solutions for the Belousov-
Zhabotinskii Reaction Diffusion System, J. Partial Diff. Eqs.,
1(1988), 61--66
C.V.Pao Monotone Methods for Numerical Solutions of Reaction
Diffusion Equations, Lecture Notes in Pure and Appl. Math., 109(1987), Dekker,
417--425
C.V.Pao Numerical Solutions for Some Coupled Systems of
Nonlinear Boundary Value Problems, Numer. Math., 51(1987), 381--394
C.V.Pao On a Coupled Reaction Diffusion System with Time Delays,
SIAM J. Math. Anal., 18(1987), 1026--1039
C.V.Pao Numerical Methods for Semilinear Parabolic Equations,
SIAM J. Numer. Anal., 24(1987), 24--35
C.V.Pao A Three-compartment Reaction System with the Effect of
Diffusion and Time Delay, Lecture Notes in Pure and Appl. Math. (Ed. by
J. H. Lightbourne and S. M. Rankin) 102, 1985, 111--114
B.P.Liu and C.V.Pao Almost Periodic Plane Wave Solutions
for Reaction Diffusion Equations, J. Math. Anal. Appl., 105(1985),
231--249
C.V.Pao , L.Zhou and X.J.Jin Multiple Solutions
of a Boundary Value Problem in Enzyme Kinetics, Advances in Appl. Math.,
6(1985), 209--229
C.V.Pao and J.M.Mahaffy Qualitative Analysis of a
Coupled Reaction Diffusion Model in Biology with Time Delays, J. Math.
Anal. Appl.,109(1985), 355--371
C.V.Pao Monotone Iterative Methods for Finite Difference System
of Reaction Diffusion Equations, Numer. Math., 46(1985), 571--586
C.V.Pao Stability Analysis of a Coupled Diffusion-Transport
System for Oxygen Transport in Blood and Tissue, Nonlin. Anal.: TMA,
9(1985), 1037--1059
C.V.Pao Asymptotic Behavior of a Reaction Diffusion System in
Bacteriology, J. Math. Anal. Appl., 108(1985), 1--14
J.M.Mahaffy and C.V.Pao Models of Genetic Control by
Repression with Time Delays and Spatial Effects, J. Math. Biol.,
20(1984), 39--57
C.V.Pao Monotone Convergence of Time-dependent Solutions for
Coupled Reaction Diffusion System, Lecture Notes in Pure and Appl. Math.
(ed. by V.Lakshmikantham), 90(1984), 455--465
C.V.Pao Stability of a Coupled Reaction Diffusion System,
{ \it J. Applicable Anal., 17(1984), 79--86
C.V.Pao Comparison and Stability of Solutions for a Neutron
Transport Problem with Temperature Feedback, SIAM J. Math. Anal.,
14(1983),167--184
B.P.Liu and C.V.Pao Periodic Solutions of Coupled
Semilinear Parabolic Boundary Value Problems, J. Nonlin. Anal.: TMA,
6(1982), 237--252
L. Zhou and C.V.Pao Asymptotic Behavior of a Competition
Diffusion System in Population Dynamics, J. Nonlin. Anal.: TMA, 6(1982),
1163--1184
C.V.Pao Asymptotic Limit and Blowing-up Behavior of Solutions
for a Reaction Diffusion System, Proc. Nonlinear Phenomena in
Mathematical Sciences(ed. by V. Lakshmikantham), 767--779, Academic Press,
1982}
C.V.Pao On Nonlinear Reaction--Diffusion Systems, { J. Math.
Anal. Appl., 87(1982), 165--198
C.V.Pao Asymptotic Stability of a Coupled Diffusion System
Arising from Gas-liquid Reactions, Rocky Mountain J. Math., 12(1982),
55--73
C.V.Pao Stability and Instability of the Energy Dependent
Diffusion System in Reactor Dynamics, Math. Meth. Appl. Sci., 3(1981),
488--505
C.V.Pao Reaction Diffusion Equations with Nonlinear Boundary
Conditions, J. Nonlin. Anal.: TMA, 5(1981), 1077--1094
C.V.Pao Coexistence and Stability of a Competition-Diffusion
System in Population Dynamics, J. Math. Anal. Appl., 83(1981), 54--76
C.V.Pao Asymptotic Stability of Reaction Diffusion Systems in
Chemical Reactor and Combustion Theory, J. Math. Anal. Appl., 82(1981),
503--526
C.V.Pao Nonexistence of Global Solutions for an Integro-
differential System in Reactor Dynamics, SIAM J. Math. Anal., 11(1980),
559--564
C.V.Pao Mathematical Analysis of Enzyme-substrate Reaction
Diffusion in Some Biochemical Systems, J. Nonlin. Anal.: TMA,
4(1980), 369--392
C.V.Pao On the Blowing-up Behavior of Solutions for a Parabolic
Boundary Value Problem, J. Applicable Anal., 10(1980), 5--13
C.V.Pao Asymptotic Behavior of Solutions for a Parabolic
Equation with Nonlinear Boundary Conditions, Proc. Amer. Math. Soc.,
80(1980), 587--593
C.V.Pao Asymptotic Stability and Non-existence of Global
Solution for a Semilinear Parabolic Equation, Pacific J. Math.,
84(1979), 191--197
C.V.Pao Bifurcation Analysis on a Nonlinear Diffusion System in
Reactor Dynamics, J. Applicable Anal., 9(1979), 107--119
C.V.Pao Asymptotic Behavior and Bifurcation Analysis for a
Nonlinear Diffusion System Arising from Gas-liquid Absorption, J.
Nonlin. Anal.: TMA, 3(1979), 101--109
C.V.Pao Positive Solution of an Integrodifferential System in
Neutron Transport with Delayed Neutrons, Rend. di Matema., 11(1978),
565--584
C.V.Pao Asymptotic Behavior and Nonexistence of Global Solutions
for a Class of Nonlinear Boundary Value Problems of Parabolic Type,
J. Math. Anal. Appl., 65(1978), 616--637
C.V.Pao The Kinetics of Diffused Substances in Some Biological
Systems, Bull. Math. Biology, 40(1977), 107--121
C.V.Pao Nonexistence of Global Solutions and Bifurcation Analysis
for a Boundary Value Problem of Parabolic Type, Proc. Amer. Math. Soc.,
65(1977), 245--251
C.V.Pao Positive Solutions of a Nonlinear Boundary-value Problem
of Parabolic Type, J. Differential Equations, 22(1976), 145--163
C.V.Pao On a Nonuniform Parabolic Equation with Mixed Boundary
Condition, Proc. Amer. Math. Soc., 49(1975), 83--89
C.V.Pao Population Growth Described by a Nonlinear Boundary Value
Problem of Parabolic Type, Z. Appl. Math. Phys., 26(1975), 453--461
C.V.Pao A Mixed Initial Boundary Value Problem Arising in
Neurophysiology, J. Math. Anal. Appl., 52(1975), 105--119
C.V.Pao Solution of a Nonlinear Integrodifferential System
Arising in Nuclear Reactor Dynamics, J. Math. Anal. Appl., 48(1974),
470--492
C.V.Pao Positive Solution of a Nonlinear Diffusion System
Arising in Chemical Reactors, J. Math. Anal. Appl., 46(1974),
820--835
C.V.Pao Successive Approximations of Some Nonlinear Initial
Boundary Value Problems, SIAM J. Math. Anal., 5(1974), 91--102