Results 71 to 80 of about 36,597 (202)
Sharp local well-posedness for KP-I equations in the semilinear regime
Forum of Mathematics, SigmaWe show sharp well-posedness with analytic data-to-solution mapping in the semilinear regime for dispersion-generalized KP-I equations on $\mathbb {R}^2$ and $\mathbb {R} \times \mathbb {T}$ .
Shinya Kinoshita +2 more
doaj +1 more source
Local Well-posedness of A Non-local Burgers Equation
, 2013 In this paper, we explore a nonlocal inviscid Burgers equation. Fixing a parameter $h$, we prove existence and uniqueness of the local solution of the equation $\InviscidBurgersNonlocal{u}$ with periodic initial condition. We also explore the blow up properties of solutions to these kinds of equations with given periodic initial data, and show that ...
Yang, Hang, Goodchild, Sam
openaire +2 more sources
Local well-posedness of semilinear space-time fractional Schrödinger equation [PDF]
Journal of Mathematical Analysis and Applications, 2019 The semilinear space-time fractional Schr dinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox $H$-functions in order to to establish some $L^s$ decay estimates. After that, we give some space-time estimates for the mild solutions from which the local well-posedness is derived on some proper ...
Xiaoyan Su, Shiliang Zhao, Miao Li
openaire +2 more sources
Macroscopic Market Making Games
Mathematical Finance, Volume 36, Issue 2, Page 352-373, April 2026.ABSTRACT Building on the macroscopic market making framework as a control problem, this paper investigates its extension to stochastic games. In the context of price competition, each agent is benchmarked against the best quote offered by the others. We begin with the linear case.
Ivan Guo, Shijia Jin
wiley +1 more source
Hybrid Reaction–Diffusion Epidemic Models: Dynamics and Emergence of Oscillations
Mathematical Methods in the Applied Sciences, Volume 49, Issue 5, Page 4074-4095, 30 March 2026.ABSTRACT In this paper, we construct a hybrid epidemic mathematical model based on a reaction–diffusion system of the SIR (susceptible‐infected‐recovered) type. This model integrates the impact of random factors on the transmission rate of infectious diseases, represented by a probabilistic process acting at discrete time steps.
Asmae Tajani +2 more
wiley +1 more source
Vortex filament solutions of the Navier-Stokes equations
, 2020 We consider solutions of the Navier-Stokes equations in $3d$ with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth curve.
Bedrossian, Jacob +2 more
core
Improved local well-posedness for the periodic “good” Boussinesq equation
Journal of Differential Equations, 2013 We prove that the "good" Boussinesq model with the periodic boundary condition is locally well-posed in the space $H^{s}\times H^{s-2}$ for $s > -3/8$. In the proof, we employ the normal form approach, which allows us to explicitly extract the rougher part of the solution.
Oh, Seungly, Stefanov, Atanas
openaire +3 more sources
On the Mean‐Field Limit of Consensus‐Based Methods
Mathematical Methods in the Applied Sciences, Volume 49, Issue 5, Page 4214-4240, 30 March 2026.ABSTRACT Consensus‐based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus‐based sampling (CBS). In this paper, we investigate the “mean‐field limit” of a class of consensus methods, including
Marvin Koß, Simon Weissmann, Jakob Zech
wiley +1 more source
Local well-posedness of nonlocal Burgers equations
Differential and Integral Equations, 2009 This paper is concerned with nonlocal generalizations of the inviscid Burgers equation arising as amplitude equations for weakly nonlinear surface waves. Under homogeneity and stability assumptions on the involved kernel it is shown that the Cauchy problem is locally well posed in $H^2(\mathbb R)$, and a blow-up criterion is derived. The proof is based
openaire +2 more sources