About

Professor Michael Salins is an Associate Professor in the Department of Mathematics & Statistics at Boston University. He is a member of the Applied Mathematics and Probability and Statistics research groups. For more information about Professor Salins, please see his personal webpage.

Research topics

• Physics
• Mathematics
• Computer Science
• Applied mathematics
• Mathematical analysis

Selected publications

• Positive probability of explosion for stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise

  arXiv (Cornell University) · 2026-05-11

  preprintOpen access1st authorCorresponding

  This paper studies the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t}(t,x)=\frac{\partial^2}{\partial x^2} u(t,x)+(u(t,x))^β+σ(u(t,x))\dot{W}(t,x)$. We consider an interval $D=[-π,π]$ under periodic boundary condition where $\dot{W}(t,x)$ is a space-time white noise and $σ(u)\approx u^γ$ near $\infty$. Our results refine existing results by identifying behavior in a previously less understood regime, where we show that if $β\in(1,3),γ\in(\fracβ{2},\frac{β+3}{4})$ or $β>1,γ\in(0,\fracβ{2}]$ then mild solutions can explode with positive probability. This paper provides a partial characterization of the explosion behavior in an intermediate parameter regime, and contribute to the understanding of the interplay between the drift and diffusion terms.

  PublisherDOI

• Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass

  arXiv (Cornell University) · 2026-04-08

  articleOpen accessSenior author

  We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of reaction-diffusion systems arising, most notably, in chemistry and biology. In the deterministic setting these assumptions are known to guarantee the global existence of solutions. In the stochastic setting, however, reaction-diffusion systems have typically been analyzed under different assumptions on the reactions that preclude many natural models, such as chemical reaction systems, and the question of global existence and uniqueness under a mass-control structure has remained open. In this work, we show that stochastically perturbing reaction-diffusion systems with triangular mass control by suitable multiplicative noise leads to solutions that exist for all time.

  PublisherOA PDF

• Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass

  arXiv (Cornell University) · 2026-04-08

  preprintOpen accessSenior author

  We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of reaction-diffusion systems arising, most notably, in chemistry and biology. In the deterministic setting these assumptions are known to guarantee the global existence of solutions. In the stochastic setting, however, reaction-diffusion systems have typically been analyzed under different assumptions on the reactions that preclude many natural models, such as chemical reaction systems, and the question of global existence and uniqueness under a mass-control structure has remained open. In this work, we show that stochastically perturbing reaction-diffusion systems with triangular mass control by suitable multiplicative noise leads to solutions that exist for all time.

  PublisherDOI

• Positive probability of explosion for stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise

  ArXiv.org · 2026-05-11

  articleOpen access1st authorCorresponding

  This paper studies the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t}(t,x)=\frac{\partial^2}{\partial x^2} u(t,x)+(u(t,x))^β+σ(u(t,x))\dot{W}(t,x)$. We consider an interval $D=[-π,π]$ under periodic boundary condition where $\dot{W}(t,x)$ is a space-time white noise and $σ(u)\approx u^γ$ near $\infty$. Our results refine existing results by identifying behavior in a previously less understood regime, where we show that if $β\in(1,3),γ\in(\fracβ{2},\frac{β+3}{4})$ or $β>1,γ\in(0,\fracβ{2}]$ then mild solutions can explode with positive probability. This paper provides a partial characterization of the explosion behavior in an intermediate parameter regime, and contribute to the understanding of the interplay between the drift and diffusion terms.

  PublisherOA PDF

• Global solutions to the stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative white noise coefficient

  Stochastic Partial Differential Equations Analysis and Computations · 2025-02-20

  article1st authorCorresponding
  PublisherDOI

• Nonexplosion for a large class of superlinear stochastic parabolic equations, in arbitrary spatial dimension

  Stochastic Partial Differential Equations Analysis and Computations · 2025-10-30

  article1st authorCorresponding
  PublisherDOI

• Preventing finite-time blowup in a constrained potential for reaction–diffusion equations

  Stochastic Processes and their Applications · 2025-03-10

  articleSenior author
  PublisherDOI

• Gaussian fluctuations for the nonlinear stochastic heat equation with drift

  ArXiv.org · 2025-12-13

  preprintOpen accessSenior author

  In this article, we prove the Quantitative Central Limit Theorem (QCLT) for the spatial average of the solution of the nonlinear stochastic heat equation with constant initial condition, driven by space-time Gaussian white noise in dimension 1. The novelty is that the equation contains a drift term. We assume that the drift and diffusion coefficients are twice differentiable with bounded first and second order derivatives. For the proof, we use Malliavin calculus, and the second-order Poincaré inequality due to Vidotto (2020). To estimate the moment of the second Malliavin derivative of the solution, we develop a novel estimate for the product of two heat kernels, which is of independent interest. Finally, we provide the functional result corresponding to this CLT.

  PublisherOA PDFDOI

• Nonexplosion for a large class of superlinear stochastic parabolic equations, in arbitrary spatial dimension

  ArXiv.org · 2025-05-02

  preprintOpen access1st authorCorresponding

  This paper explores the finite time explosion of the stochastic parabolic equation $\frac{\partial u}{\partial t}(t,x)=Au(t,x)+σ(u(t,x))\dot{W}(t,x)$ in arbitrary bounded spatial domain with a large class of space-time colored noise under Neumann, periodic or Dirichlet boundary conditions where $A$ is second-order self-adjoint elliptic operator and $σ$ grows like $σ(u)\approx C(1+|u|^χ)$ where $χ=1+\frac{1-η}{2β}$ with $η$ and $β$ are the parameters related to the singularities of heat kernel and noise covariance kernel. We improve upon previous results by proving the theory in arbitrary spatial dimension, general elliptic operator, general space-time colored noise, a larger class of boundary conditions and proves that $χ$ can reach the level $1+\frac{1-η}{2β}$.

  PublisherOA PDFDOI

• Uniform attraction and exit problems for stochastic damped wave equations

  ArXiv.org · 2025-02-03

  preprintOpen access

  We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet boundary conditions, continuous initial position and distributional initial velocity. In the first part of this work, we study the corresponding deterministic dynamics and prove that certain neighborhoods of asymptotically stable equilibria are uniformly attracting in the topology of uniform convergence. Then, we consider exit problems for local solutions of the stochastic damped wave equations from bounded domains $D$ of uniform attraction. Using tools from large deviations along with novel controllability results, we obtain logarithmic asymptotics for exit times and exit places, in the vanishing noise limit, that are expressed in terms of the corresponding quasipotential. In doing so, we develop arguments that take into account the lack of both smoothing and exact controllability that are inherent to the problem at hand. Moreover, our exit time results provide asymptotic lower bounds for the mean explosion time of local solutions. We introduce a novel notion of "regular" boundary points allowing to avoid the question of boundary smoothness in infinite dimensions and leading to the proof of a large deviations lower bound for the exit place. We illustrate this notion by providing explicit examples for different classes of domains $D$. Conditions under which lower and upper bounds for exit time and exit place logarithmic asymptotic hold, are also presented. In addition, we obtain deterministic stability results for linear damped wave equations that are of independent interest.

  PublisherOA PDFDOI

Frequent coauthors

• Konstantinos Spiliopoulos

  17 shared

• Sandra Cerrai

  12 shared

• Carl Mueller

  University of Rochester

  5 shared

• Eyal Neuman

  5 shared

• Paul Dupuis

  4 shared

• Wenqing Hu

  Wuhan University

  3 shared

• Zsolt Pajor-Gyulai

  3 shared

• Mark Freidlin

  3 shared