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Research

Research Areas

Nonlinear Partial Differential Equations, Applied Analysis: Theory and Algorithms

Research Interests
  • The Mathematics of Fluids
  • Multiphase Flows, Fluid-Particle Interaction, Plasma Physics
  • Phase Transitions
  • The Dynamics of Tumor Growth: Modeling, Analysis, Simulations
  • Quantum Dynamics, Quantum Algorithms
  • Hyperbolic Conservation Laws
  • Variational Problems
  • Applications to Material Science, Fluid Dynamics and Math Biology
Journal Articles
  • P. Jayanti and K. Trivisa, Uniqueness in a Navier-Stokes-nonlinear-Schrödinger model of superfluidity. Nonlinearity 35 (2022) no. 7, 3755-3776.
  • P. Jayanti and K. Trivisa, Local existence of solutions to a Navier-Stokes-nonlinear-Schrödinger model of superfluidity. J. Math. Fluid Mech. 24 (2022), no. 2, Paper No. 46, 41 pp.
  • J.-P. Liu, H.-O. Kolden, H.K. Krovi, N.F. Loureiro, K. Trivisa and A. Childs, Efficient quantum algorithm for dissipative, weakly nonlinear differential equations. PNAS (2021), Vol. 118, no. 35.
  • M.Coti Zelati, N.Glatt-Holtz, and K. Trivisa, Invariant Measures for the Stochastic One-Dimensional Compressible Navier-Stokes Equations. Journal Appl. Math. Optim. 83 (2021) no. 3, 1487-1522. arXiv:1802.04000.
  • P. Jayanti and K. Trivisa, Global regularity of the 2D HVBK equations. Journal of Non- linear Science, 31 (2021), no. 1.
  • D. Donatelli, T. Thorsen and K. Trivisa, Weak dissipative solutions to a free-boundary problem for finitely extensible bead-spring chain molecules: variable viscosity coefficients, Kinetic Rel. Models (2020), no. 5, 1047–1070.
  • 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, (2020) 482.
  • D. Donatelli and K. Trivisa, Recent advances in the mathematical modeling for tumor growth. SEMA-SIMAI Springer Series (2018).
  • 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, 4245–4286.
  • 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).
  • 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.
  • 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 (2018).
  • 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.