## 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). L^{2} 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.