Alex Himonas

Professor

Education

B.S., Patras University, Greece, 1976
M.S., Purdue University, 1982
Ph.D., Purdue University, 1985

Research Group

Partial Differential Equations

Research Area

Partial Differential Equations

Bio

Research Interests

Partial differential equations (PDE) studying fundamental questions like existence and uniqueness of solution, stability, and regularity properties. Many of these PDE arise in mathematical physics and some model finance and economics situations.

Selected Publications

• A. Himonas and F. Yan, A higher dispersion KdV equation on the half-line. J. Differential Equations  333 (2022) 55–102.
• A. Himonas and D. Mantzavinos, Well-posedness of the Nonlinear Schrödinger equation on the half-plane. Nonlinearity. 33 (2020) 5567—5609.
• A. Himonas, C. Holliman and C. Kenig, Construction of 2-peakon solutions and ill-posedness for the Novikov equation. SIAM J. Math. Anal., 50, No. 3, (2018), 2968– 3006.
• A. Fokas, A. Himonas & D. Mantzavinos, The nonlinear Schrödinger equation on the half-line. Trans. Amer. Math. Soc. 369 (2017), no. 1, 681–709.
• A. Fokas, A. Himonas & D. Mantzavinos, The Korteweg–de Vries equation on the half-line. Nonlinearity 29 (2016), no. 2, 489–527.
• F. Barostichi, A. Himonas & G. Petronilho, Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems. J. Funct. Anal. 270 (2016), no. 1, 330–358.
• A. Himonas, C. Holliman & K. Grayshan, Norm inflation and ill-posedness for the Degasperis-Procesi equation. Comm. Partial Differential Equations 39 (2014), no. 12, 2198–2215.
• A. Himonas & G. Misiołek, Non-uniform dependence on initial data of solutions to the Euler equations of hydrodynamics. Comm. Math. Phys. 296 (2010), no. 1, 285–301. 
• A. Himonas & C. Kenig, Non-uniform dependence on initial data for the CH equation on the line. Differential Integral Equations 22 (2009), no. 3-4, 201–224.
• A. Himonas, G. Misiołek, G. Ponce & Y. Zhou, Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Comm. Math. Phys. 271 (2007), no. 2, 511–522.
• O. Calin, Y. Chen, T. Cosimano & A. Himonas, Solving asset pricing models when the price-dividend function is analytic. Econometrica 73 (2005), no. 3, 961–982.
• A. Himonas & G. Petronilho, Global hypoellipticity and simultaneous approximability.  J. Funct. Anal. 170 (2000), no. 2, 356–365.
• N. Hanges & A. Himonas, Singular solutions for sums of squares of vector fields. Comm. Partial Differential Equations 16 (1991), no. 8-9, 1503–1511.
• A. Himonas, Semirigid partial differential operators and microlocal analytic hypoellipticity. Duke Math. J. 59 (1989), no. 1, 265–287.