Research Area
Research Interests
Publications
Nonlinear Partial Differential Equations, Applied Analysis
The Mathematics of Fluids
Multiphase Flows, Fluid-Particle Interaction, Phase Transitions
The Dynamics of Tumor Growth: Modeling, Analysis, Simulations
Hyperbolic Conservation Laws
Variational Problems
Applications to Material Science, Fluid Dynamics and Math Biology
Journal Articles:
D. Donatelli, T. Thorsen and K. Trivisa, Weak dissipative solutions to a free-boundary problemfor finitely extemnsible bead-spring chainmolecules: variable viscosity coefficients. To appear in Kinetic and Related Models (2020).
H. Ueda, K. Stephens, K. Trivisa and W. Bentley, Bacteria floc, but do they flock? Insights from population interaction models of quorum sensing. mBio (2019), Vol. 10, no. 3 (2019).
D. Donatelli and K.Trivisa, On a free boundary problem for finitely extensible bead-spring chain molecules in dilute polymers. J. Math. Anal. Appl. no. 1, 482 (2020)
M.Coti Zelati, N.Glatt-Holtz, and K. Trivisa, Invariant Measures for the Stochastic One-Dimensional Compressible Navier-Stokes Equations. To appear in the Journal Applied Mathematics and Optimization (2020) arXiv: 1802.04000.
D. Donatelli and K. Trivisa, On the vanishing viscosity approximation of a nonlinear model for tumor growth. Dynamics of Partial Differential Equations 15 (2018), no. 2, 411-465.
R. Nochetto, K. Trivisa and F.Weber, On the dynamics of ferrofluids: Global weak solutions
to the Rosensweig system and rigorous convergence to equilibrium. SIAM J. Math. Anal. 51 (2019) no.6, 4245
K. Trivisa and F. Weber, Analysis and simulations on a model for the evolution of tumors under the influence of nutrient and drug application. To appear in SIAM Journal of Numerical Analysis 56 (2018) no. 1 542–569.
pdf.
S.Smith and K. Trivisa, The Stochastic Navier-Stokes Equations for Heat Conducting, Compressible Fluids: Global Existence of Weak Solutions. J. Evol. Equ. (2018) 15 (2018), no. 2, 411-465. pdf.
D. Donatelli and K. Trivisa, On a free boundary problem for polymeric fluids: Global existence of weak solutions. NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 5, Art. 51, 20 pp.
K. Trivisa and F. Weber, A convergent explicit finite difference scheme
for a mechanical model for tumor growth. Mathematical Modeling and Numerical Analysis 51 (2017) no. 1 35-62 .
pdf.
D. Donatelli and K. Trivisa, Recent advances in the mathematical modeling for tumor growth. To appear in SEMA-SIMAI Springer Series(2018)
D. Donatelli and K. Trivisa, On a nonlinear model for tumor growth in a cellular medium. To appear in Journal of Dynamics and Differential Equations (2015).
D. Donatelli and K. Trivisa, On a nonlinear model for tumor growth with drug application. To appear in Nonlinearity 28 (2015), 1463-1481.
S. Doboszczak and K. Trivisa, On a fluid-particle interaction model in a moving domain: Global existence of weak solutions. J. Fields Institute Communications (2015), 111-133.
D. Donatelli and K. Trivisa, On a nonlinear model for tumor growth. Global in time weak solutions. J. Math. Fluid Mech. 16 no. 6 (2014), 1017-1043.
A. Miroshnikov and K. Trivisa, Stability and convergence of relaxation schemes for hyperbolic balance laws. J. Hyperbolic Differential Equations 12, no.1 (2015), 189-219.
T. Karper, A. Mellet and K. Trivisa, Hydrodynamic Limit of the Kinetic Cucker-Smale Model. Math. Models Methods Appl. Sci. 25 (2015), no. 1, 131-163.
D. Donatelli and K. Trivisa, On a nonlinear model for tumor growth. Global in time weak solutions. J. Math. Fluid Mech. 16, no. 6 (2014), 1017-1043.
J. Ballew and K. Trivisa, Viscous and inviscid models in fluid-particle interaction. Communications in Information and Systems}, 13 (2014), no. 1, 45--78.
A. Miroshnikov and K. Trivisa, Relative entropy method in hyperbolic relaxation for balance laws. Commun. Math. Sci. 12, no. 6, (2014), 1017-1043.
J. Ballew and K. Trivisa, Weakly dissipative solutions and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system. Nonlinear Analysis: Theory, Methods & Applications 91 (2013), 1-19.
H.Bae and K. Trivisa, On the Doi Model for the Suspensions of Rod-Like Molecules: Global-in-time Existence. Commun. Math. Sci. 11, no. 3, (2013), 831-850.
Y.-S. Kwon and K. Trivisa, On the incompressible limit problems for multicomponent reacting flows. Quarterly of Applied Mathematics 71, (2013), 37-67.
T. Karper, A. Mellet and K. Trivisa, Hydrodynamic Limit of the Kinetic Cucker-Smale Model. Math. Models Methods Appl. Sci. 25 (2015), no. 1, 131-163.
D. Levermore, W. Sun and K. Trivisa, Singular Limit of a Dispersive Navier-Stokes System with an Entropy Structure. Analysis and Applications 13 no.1 (2015), 77-99.
T. Karper, A. Mellet and K. Trivisa, Existence of Weak Solutions to Kinetic Flocking Models. SIAM J. Math. Anal. (2013) no. 1, 215-243.
T. Karper, A. Mellet and K. Trivisa, On strong local alignment in the kinetic Cucker-Smale model.
Springer Proc. Math. & Stat. (2013) .
L. Cesbron, A. Mellet and K. Trivisa, Anomalous transport of particles in plasma physics.
Appl. Math. Lett. 25, no.12 (2012)
J. Ballew and K. Trivisa, Suitable weak solutions & low stratification limit to a fluid-particle interaction model. Quarterly of Applied Mathematics 3, (2012) 469-494.
H. Bae and K. Trivisa, On the Doi Model for the Suspensions of
Rod-Like Molecules in Compressible Fluids. Math. Methods Appl. Sci. 10 (22) (2012)
C.D. Levermore, W. Sun and K. Trivisa, Low Mach number limit from
a dispersive Navier-Stokes system to Sone's Ghost Effect System.
SIAM J. Math. Anal. (2012).
pdf.
C. Christoforou and K. Trivisa.
Decay of positive waves of hyperbolic balance laws.
Acta Math. Sci. Ser. B Engl. Ed. 32 no. 1 (2012) 352-366.
C. Christoforou and K. Trivisa.
On the convergence rate for vanishing viscosity approximations
to hyperbolic balance laws. SIAM
J. Math. Anal. 43 (2011), no. 5, 2307-2336
pdf.
J. Carrillo, T. Karper and K. Trivisa.
On the Dynamics of a Fluid-Particle Interaction Model: The
Bubbling Regime. Nonlinear Analysis: Theory, Methods &
Applications 74 (2011) 2778-2801.
pdf.
Y.-S. Kwon and K. Trivisa.
Stability and Large Time Behavior for Multicomponent Reactive
Flows.
Nonlinearity, 22, no. 10, (2009) 2443-2471.
C. Christoforou and K. Trivisa.
Sharp Decay Estimates for Hyperbolic Balance Laws.
J. Differential Equations, 247, no. 2, (2009) 401-423.
D. Donatelli, K. Trivisa.
From the Dynamics of Gaseous Stars to
the Incompressible Euler Equations.
J. Differential Equations, 245, (2008) 1356-1385.
E. Feireisl, H. Petzeltova and K. Trivisa.
Multicomponent reactive flows: Global-in-time existence for large data.
Comm. Pure Appl. Anal., 7, no.5, (2008) 1017-1047.
K. Trivisa.
On the Dynamics of Liquid-Vapor Phase Transition.
SIAM J. Math. Anal Vol. 39, 6, (2008), 1788-820.
K. Trivisa.
On Binary Fluid Mixtures.
Contemp. Math., Amer. Math. Soc., Vol. 429, (2007), 257-278.
D. Donatelli and K. Trivisa.
On the Motion of a Viscous Compressible Radiative-Reacting Gas.
Comm. Math. Phys. 265, (2006), 463-491.
D. Donatelli and K. Trivisa.
On a Multidimensional Model for the Combustion of
Compressible Reacting Fluids.
Arch. Ration. Mech. Anal. 185, (2007), 379-408.
dvi.
G.-Q. Chen and K. Trivisa.
Analysis on Models for Exothermically, Reacting, Compressible Flows
with Large Discontinuous Initial Data.
Contemp. Math., 371, (2004), 71-89.
P. G. LeFloch and K. Trivisa.
Continuous Glimm-Type Functionals and Spreading of Rarefaction Waves.
Commun. Math. Sci., 2, no. 2. (2004), 213-236. pdf.
G.-Q. Chen, D. Hoff and K. Trivisa.
Analysis on a Model for the Dynamic Combustion of a Compressible,
Reacting Fluid.
Hyperbolic problems: theory, numerics, applications,
Springer-Verlag, ISBN: 3-540-44333-9, (2003), 409-418.
(Editors T.Y. Hou and E. Tadmor)
K. Trivisa.
Global Existence and Asymptotic Analysis of Solutions to a Model for
the Dynamic Combustion of Compressible Fluids.
Discrete Contin. Dyn. Syst., Vol. 1078-0947, (2003), 852-863.
K. Trivisa.
BV Estimates for NxN Systems of Conservation Laws.
Contemp. Math., 327, (2003), 341-358
pdf.
G.-Q. Chen, D. Hoff and K. Trivisa.
Global Solutions to a Model for Exothermically
Reacting, Compressible Flows with Large
Discontinuous Initial Data.
Arch. Ration. Mech. Anal., 166, (2003), 321-358
pdf.
G.-Q. Chen, D. Hoff and K. Trivisa.
On the Navier-Stokes Equations for Exothermically Reacting
Compressible fluids. Acta Math. Appl. Sinica, Vol. 18, No. 1 (2002), 15-36.
pdf.
M. Lewicka and K. Trivisa.
On the L1 Well-Posedness of Systems of
Conservation Laws Near Solutions Containing Two
Large Shocks. Journal of Differential Equations, Vol. 179, No. 1, (2002),
133-177
pdf.
G.-Q. Chen, D. Hoff and K. Trivisa.
Global Solutions of the Compressible Navier-Stokes
Equations with Large Discontinuous Initial
Data.
Comm. Partial Differential
Equations, 25, No. 11-12 (2000), 2233 - 2257
dvi or
pdf.
B. Dacorogna, I. Fonseca, J. Maly and K. Trivisa.
Manifold Constrained Variational Problems
Calc. Var. Partial Differential
Equations, 9, No. 3 (1999), 185-207.
dvi or
pdf.
K. Trivisa.
Decay & Uniqueness of Solutions of Hyperbolic Systems of Conservation
Laws via Generalized Characteristics.
Hyperbolic problems: theory, numerics, applications, Vol. II,
963-972, Internat. Ser. Numer. Math., 130,
Birkhaeuser, Basel (1999), (Editors M. Fey and R. Jeltsch)
K. Trivisa. A Priori Estimates in Hyperbolic Systems of Conservation Laws via
Generalized Characteristics. Comm. Partial Differential
Equations, 22, No. 1-2 (1997), 235-267.