Education
A.B.: University of California Berkeley, 1967
M.A.: University of Wisconsin Madison, 1970
Ph.D.: Univ. of Wisconsin, Madison 1971
Research Support
1964 University of California, Berkeley Type:Fellowship
1970 University of Wisconsin-Madison Type:Fellowship
1975 University of Cincinnati Taft Faculty Research Type:Grant
1980 -1982 NSF Research Type:Grant
1985 University of Cincinnati Taft Faculty Research Type:Grant
1993 Universidad Nacional, Bogata Type:Grant
1995 Colciencias Colombia Type:Grant
Abbreviated Publications
Peer Reviewed Publications
(1973). Connection formulas for asymptotic solutions for second order turning points in unbounded domains. SIAM J. Math. Anal., 4, 89-103.
(1973). Studies on doubly asymptotic series solutions for differential equations in unbounded domains. J. Math. Anal. Appl., 44, 238-263.
(1974). Doubly asymptotic series for the n-th order differential equations in unbounded domains. SIAM J. Math. Anal., 5, 187-201.
(1975). Lateral connections for asymptotic solutions for higher order turning points in unbounded domains. J. Math. Anal. Appl., 50, 560-578.
(1976). A doubly asymptotic existence theorem and application to order reduction. Proc. London Math. Soc., 3(33), 151-176.
(1976). Limiting behavior for several interaction populations. Math. Biosci., 29, 85-98.
(1977). Distribution of eigenvalues in the presence of higher turning points. Trans. Amer. Math. Soc., 229, 111-135.
(1977). Periodic solutions for a prey-predator differential delay equation. J. Diff. Eqns., 26, 391-403.
(1978). A third order linear differential equation on the real line, with two turning points. J. Diff. Eqns., 29, 304-328.
(1978). Limiting behavior for a prey-predator model with diffusion and crowding effects. J. Math. Biol., 6, 87-93.
(1979). Conditions for global stability concerning a prey-predator model with delay effects. SIAM J. Appl. Math., 36, 281-286.
(1980). Equilibria and stabilities for competing species reaction-diffusion equations with Dirichlet boundary data. J. Math. Anal. Appl., 73, 204-218.
(1981). Stabilities for equilibria of competing-species reaction-diffusion equations with homogeneous Dirichlet condition. Funk. Ekv. (Ser. Internat.), 24, 201-210.
(1982). A semilinear reaction-diffusion prey-predator system with nonlinear coupled boundary conditions: equilibrium and stability. Indiana Univ. Math. J., 31, 223-241.
(1982). Monotone schemes for semilinear elliptic systems relative to ecology. Math. Methods in Appl. Sciences, 4, 272-285.
(1983). The reaction-diffusion system of competing populations, singularly perturbed by small diffusion rates. Rocky Mountain J. Math., 13, 177-190.
(1984). A study of three species population reaction-diffusion equations by monotone schemes. J. Math. Anal. Appl., 100, 583-604.
(1984). Nonlinear density-dependent diffusion for competing species interaction: large-time asymptotic behavior. Proceedings of Edinburgh Math. Soc., 27, 131-144.
(2001). Positive solutions for systems of PDE and optimal control. J. Nonlinear Analysis, 47, 1345-1356.
(2003). Asymptotically stable invariant manifold for coupled parabolic-hyperbolic partial differential equations. J. Diff. Eqns., 187, 184-200.
(2003). Bifurcating positive stable steady-states for a system of damped wave equations. Differential and Integral Equations, 16, 453-471.
(2004). Positive solutions for large elliptic systems of interacting species groups by cone index methods. J. Math. Anal. Appl., 291, 302-321.
(2005). Stable invariant manifolds for coupled Navier-Stokes and second-order wave systems. Asymptotic Analysis, 43, 339-357.
(1993). Optimal control for nonlinear systems of partial differential equations related to ecology. Proceedings for Third International Colloquium on Differential Equations, International Science Publishers, Netherland.
(1995). Optimal harvesting-coefficient control of steady-state prey-predator diffusuive Volterra-Lotka systems. Applied Mathematics & Optimization, 31, 219-241.
(1997). Reaction-diffusion systems with temperature feedback: bifurcations and stability. Proceedings of World Congress of Nonlinear Analysis 96, J. Nonlinear Analysis. 30, 3379-3390.
(1998). Diffusion-reaction systems in neutron-fission reactors and ecology. Nonlinear Diffusion Equations and Their Equilibrium States II, Math. Sciences Research Institute Publ., edited by W.M. Ni, L.A. Peleiter and J. Serrin, Springer-Verlag.
Murio, D. & Smith, B.D. (1994). Stability analysis for cone-beam reconstruction. Proc. of Second International Dynamic System Identification and Inverse Problems, edited by O. Alifanov. St. Petersburg, 2, F5.1-F5.12.
Xu, R. (1992). Stability criteria for multiple limit cycles. Dynamic Systems and Applications, 1, 283-315.
Bendjijlali, B. (1986). N competing species with one prey in heterogeneous environment under Neumann boundary conditions: steady states and stability. SIAM Appl. Math., 46, 81-98.
Chen, G.S. (1984). Positive solutions for temperature-dependent two-group neutron flux equations: equilibrium and stabilities. SIAM J. Math. Anal., 15, 490-499.
Chen, Gen S. (1985). Nonlinear multigroup neutron-flux systems: blow-up, decay and steady states. Math. Phys., 26, 1553-1559.
Chen, Gen S. (1986). Elliptic and parabolic systems for neutron fission and diffusion. J. Math. Anal. Appl., 120, 655-669.
Chen, Gen S. (1989). Positive solutions for reactor multigroup neutron transport systems: criticality problem. SIAM J. Appl. Math., 49, 871-887.
Chen, Gen S. (1991). Nonlinear reactor multigroup neutron transport system: existence and stability problems. J. Math. Phys., 32, 905-915.
Chen, Gen S. (1999). Optimal control of multigroup neutron fission systems. Applied Math. & Optimization, 40, 39-60.
Chen, Gen S. (2005). Existence and global bounds for a fluid model of plasma display technology. J. Math. Anal. Appl, 310, 436-458.
Clark, D. (1980). Bifurcations and large-time asymptotic behavior for prey-predator reaction-diffusion equations with Dirichlet boundary data. J. Diff. Eqns., 35, 113-127.
Fan, G. (1990). Existence and stabilities of periodic solutions for competing-species diffusion systems with Dirichlet boundary conditions. J. Applicable Analysis, 39, 119-149.
Fan, G. (1990). Positive solutions for degenerate and non-degenerate elliptic systems: existence and numerical approximations. Asymptotic and Computational Analysis, edited by R. Wong, Marcel Dekker, N.Y.
He, F, & Stojanovic, S. (1995). Periodic optimal control for parabolic Volterra-Lotka type equations. Math. Methods in Appl. Sciences, 18, 127-146.
He. F., & Stojanovic, S. (1994). Periodic optimal control for competing parabolic Volterra-Lotka type systems. J. Comp. & Appl. Math., 52, 199-217.
Hou, X. & Li, Y. (2008). Exclusive traveling waves for competitive reaction-diffusion system and their stabilities. J. Math. Anal. Appl., 338, 902-924.
Hou, X. (2008). Traveling waves solutions for a competitive reaction-diffusion system and their asymptotics. J. Nonlinear Anal., Series B: Real World., 5, 2196-2213.
Korman, P. & Stojanovic, S. (1990). Monotone iterations for nonlinear obstacle problem. J. Australian Math. Soc. Series B., 31, 259-276.
Korman, P. (1986). A general monotone scheme for elliptic systems with applications to ecological models. Proc. of Royal Soc. of Edinburgh, 102A, 315-325.
Korman, P. (1987). On the existence and uniqueness of positive steady-states in the Volterra-Lotka ecological models with diffusion. J. Applicable Analysis, 26, 145-159.
Lazer, A.C., & Murio, D.A. (1982). Monotone scheme for finite difference equations concerning steady-state prey-predator interactions. J. Computational and Appl. Math., 8, 243-252.
Leung, S. (1987). A general alternating scheme for systems of equations. Internat. J. Math. Educ. in Sci. and Tech., 18, 9-14.
Meyer, K. (1974). Adiabatic invariants for linear Hamiltonian systems, with a question by Voros and a reply by Meyer. Geometrie symplectique et physique mathematique, Colloques Internationaux de Centre National de la Recherche Scientifique, 237, 137-145.
Meyer, K. (1975). Adiabatic invariants for linear Hamiltonian systems. J. Diff. Eqns., 17, 23-43.
Murio, D. (1986). Accelerated monotone scheme for finite difference equations concerning steady state prey-predator interactions. J. Computational and Appl. Math., 16, 333-341.
Murio, D. (1986). L2 convergence for positive finite difference solutions of the diffusive logistic equation in two dimensional bounded domains. International J. Comp. & Math. with Appl., 12A, 991-1005.
Murio, D.A. (1980). Monotone scheme for finite difference equations concerning steady-state competing-species interactions. Portugaliae Mathematica, 39, 497-510.
Ortega, L. (1995). Bifurcating solutions and stabilities for multigroup neutron fission systems with temperature feedback. J. Math. Anal. Appl., 194, 489-510.
Ortega, L. (1996). Positive steady-states for large systems of reaction-diffusion equations: synthesizing from smaller subsystems. Canadian Applied Math. Quarterly. 4, 175-195.
Ortega, L. (1998). Existence and monotone scheme for T-periodic nonquasimonotone reaction-diffusion systems, application to autocatalytic chemistry. J. Math. Anal. Appl., 221, 712-733.
Stojanovic, S. (1990). Direct methods for distributed games. Differential and Integral Equations, 3, 1099-1111.
Stojanovic, S. (1993). Optimal control for elliptic Volterra-Lotka equations. J. Math. Anal. Appl., 173, 603-619.
Villa, B. (1997). Reaction-diffusion systems for multigroup neutron fission with temperature feedback, positive steady-state and stability. Differential and Integral Equations. 10, 739-756.
Villa, B. (2000). Asymptotically stable positive periodic solutions for parabolic systems with temperature feedback. J. Nonlinear Analysis, 41, 75-95.
Villa, B. (2000). Bifurcation of reaction-diffusion systems, application to epidemics of many species. J. Math. Anal. Appl., 244, 542-563.
Wang, A. (1976). Analysis of models for commercial fishing: Mathematical and economical aspects. Econometrica, 44, 295-303.
Zhang, Qin (1998). Reaction-diffusion equations with nonlinear boundary conditions, blow-up and steady states. Math. Methods in Appl. Sciences, 21, 1593-1617.
Zhang, Qin (2001). Finite extinction time for nonlinear parabolic equations with nonlinear mixed boundary data. J. Nonlinear Analysis, 44, 843.
Zhang, Qin. (1998). Finite extinction time for nonlinear parabolic equations with nonlinear mixed boundary data. J. Nonlinear Analysis, 31, 1-13.
Zhou, Z. (1988). Global stability for large systems of Volterra-Lotka type integro-differential population delay equations. J. Nonlinear Analysis, 12, 495-505.
(2011) X. Hou & W. Feng, Traveling wave solutions for Lotka-Volterra systems revisited, Discrete and Continuous Dynamical Systems, Ser. B, No. 1, 171-196.
Other Publication
(1975). Adiabatic invariants for linear Hamiltonian systems. International Conference on Differential Equations. Academic Press.
(1980). Connection formulas and behavior in the large for solutions of linear differential equations depending singularly on a parameter. Singular Perturbations Asymptotics, Math. Research Center Symposia and Advanced Seminar Series. Academic Press.
(1983). Monotone schemes for three species prey-predator reaction-diffusion. Lecture Notes in Biomathematics, 52. Springer-Verlag.
Villa, B. (2000). Bifurcation of reaction-diffusion systems related to epidemics. Electronic J. of Diff. Eqs.
Book
(1989). Systems of Nonlinear Partial Differential Equations, Applications to Biology and Engineering. Dordrecht/Boston/London: Kluwer Academic Publishers.
(2009). Nonlinear Systems of Partial Differential Equations, Applications to Life and Physical Sciences, World Scientific Publishing Co., New Jersey/Singapore/London.
Presentations
Invited Presentations
(2005. ) University of Texas-Pan American,
(2002. ) International Conference on Nonlinear Partial Differential Equations .Hong Kong.
(2000. ) World Congress of Nonlinear Analysts .Catania, Italy.
(01-1999. ) University of Miami,
(1997. ) PhD Centennial Conference , University of Wisconsin, Madison.
(1996. ) World Congress of Nonlinear Analysts .Athens, Greece.
(01-1995. ) AMS Annual Meeting .
(10-1993. ) Univ. of Tennessee,
(08-1993. ) Univ. Nacional, Colombia.
(06-1993. ) Symposium on Comparison Methods and Stability .Univ. of Waterloo, Canada.
(08-1992. ) Third International Colloquium on Differential Equations .Bulgaria.
(03-1990. ) AMS Regional Meeting .Kansas.
(06-1989. ) International Symposium on Asymptotic and Computational Analysis .Manitoba, Canada.
(06-1988. ) Conference on Reaction Diffusion Equations .Heriot-Watt University, Scotland.
(08-1986. ) Math. Sciences Research Institute .Berkeley, California.
(04-1986. ) AMS Regional Meeting .Indiana.
(05-1985. ) MRC Colloquium .Madison,
(01-1985. ) Zhongshan University, China.
(12-1984. ) Tsinghua University, Taiwan.
(11-1983. ) AMA Regional Meeting .Ohio.
(06-1982. ) International Conference on Population Biology .Alberta, Canada.
(11-1981. ) Oberwolfach Conference on Math., Biology .West Germany,
(1980. ) MRC Symposium on Singular Perturbations and Asymptotics .Madison,
(1979. ) International Conference on Differential Equations .Univ. of Michigan,
(1974. ) International Conference on Differential Equations .USC,
Keywords
Partial Differential Equations, Ordinary Differenttial Equations, Applications to Biological and Physical Sciences. Elliptic, Parabolic and Hyperbolic Systems. Reaction-Diffusion Systems and Optimal Control.