# Publications

**MP**(2022)*Dispersive Approximation of Shock Waves.*Journal of Applied Mathematics and Physics (ZAMP).

**MP**and I Timofeyev (2022)*Self-Sustained Price Bubbles Driven by Digital Currency Innovations and Adaptive Behavior.*Springer Nature: Economics & Finance.

P Bedekar, A Warmflash, I Timofeyev and

**MP**(2021)*Reaction-Diffusion Models for Morphological Patterning of hESCs.*Journal of Mathematical Biology.

**MP**(2021)*A Model of Cultural Evolution in the Context of Strategic Conflict.*AIMS Journal of Kinetic and Related Problems.

**MP**(2020)*Classical Solutions of Hyperbolic Systems of PDEs with Kinetic Structure.*SIAM Journal of Mathematical Analysis.

**MP**(2020)*A Model of Discrete Choice Based on Reinforcement Learning under Short-term Memory.*Journal of Mathematical Psychology.

**MP**(2019)*Adaptive Learning in Large Populations.*Journal of Mathematical Biology.

**MP**and I Timofeyev (2019)*Asynchronous Stochastic Price Pump,*Physica A: Statistical Mechanics and Applications.

[Book chapter] Handbook of Mathematical Analysis in Mechanics of Viscous Flows

Topics on Compressible Navier-Stokes Equations Société mathématique de France, 2016.

**MP**(2016)*An Integral Representation of Functions in Gas-Kinetic Models.*Journal of Applied Mathematics and Physics (ZAMP).

**MP**(2016)*A Kinetic Model for Approximately Isentropic Solutions of the Euler Equations,*Journal of Differential Equations.

**MP**(2015)*On a Kinetic Formulation for the Euler Equations,*SIAM Journal of Mathematical Analysis.

GQ Chen and

**MP**(2015)*Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Data,*Communications in Mathematical Physics.

**MP**(2014)*A Note on Strong Solutions to the Variational Kinetic Equation for Scalar Conservation Laws,*Journal Hyperbolic Differential Equations.

**MP**(2014)*Weak Solutions of the Navier-Stokes Equations for Compressible Flows in a Half-space with No-slip Boundary Conditions,*Archive Rational Mechanics and Analysis.

GQ Chen and

**MP**(2012)*Shallow Water Equations: Viscous Solutions and Inviscid Limit.*Journal Applied Mathematics and Physics (ZAMP).

D Hoff and

**MP**(2012)*Boundary Tangency for Density Interfaces in Compressible Viscous Fluid Flows.*Journal Differential Equations.

GQ Chen and

**MP**(2010*) Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations for Compressible Fluid Flow,*Communications in Pure and Applied Mathematics.

**MP**(2010)*Asymptotics Toward Rarefaction Waves and Vacuum for 1-d Compressible Navier–Stokes Equations*, SIAM Journal of Mathematical Analysis.

**MP**(2010)*Model Problem for the Motion of a Compressible, Viscous Flow with the No-slip Boundary Condition,*Journal Applied Mathematics and Physics (ZAMP).

**MP**(2010)*An Ill-posed Problem for the Navier-Stokes Equations for Compressible Flows,*Discrete Continuous Dynamical Systems.

D Hoff and

**MP**(2009)*Instantaneous Boundary Tangency and Cusp Formation in Two-dimensional Fluid Flow, SIAM Journal of Mathematical Analysis.*

**MP**(2006)*On the Global Existence of Weak Solutions for the Navier–Stokes Equations of Compressible Fluid Flows**,*SIAM Journal of Mathematical Analysis.

H Frid and

**MP**(2004)*Spatially Periodic Solutions in Relativistic Isentropic Gas Dynamics,*Communications in Mathematical Physics.

**MP**and V. Shelukhin (1998)*On Global Solutions of a Boundary-Value Problem for the One-dimensional Buckley-Leverett Equations,*Applicable Analysis.

P Murphy, I Timofeyev, O Igoshin and

**MP**(2022)*A Mean-Field Model for Nematic Alignment of Self-Propelled Rods,*in review, Physical Review E.

**MP**(2021)*General-Purpose Cooperativeness and Altruism in Humans: Elements of the Mathematical Framework for the Interdependence Hypothesis,*in review, Biological Theory.

**MP**(2021)*Psychological Dimension of Adaptive Trading in Cryptocurrency Markets,*in review, Journal of Empirical Finance.

**MP**(2021)*Investing in a Cryptocurrency Price Bubble: Speculative Ponzi Schemes and Cyclic Stochastic Price Pumps,*in review, Journal of Behavioral Finance