Analytic Expressions of the Solutions of Advection-Diffusion Problems in One Dimension with Discontinuous Coefficients
DOI10.1137/18M1164500zbMath1495.65014OpenAlexW2779272663MaRDI QIDQ5197539
Antoine Lejay, Géraldine Pichot, Lionel Lenôtre
Publication date: 18 September 2019
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/18m1164500
discontinuous coefficientsadvection-diffusion problemsresolvent kernelstransition density functionsparticle tracking techniques
Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) PDEs with low regular coefficients and/or low regular data (35R05) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic particle methods (65C35)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers
- Sturm-Liouville operators with measure-valued coefficients
- Simulation of a stochastic process in a discontinuous layered medium
- Differential movement and movement bias models for marine protected areas
- Occupation and local times for skew Brownian motion with applications to dispersion across an interface
- On discontinuous Dirac operator with eigenparameter dependent boundary and two transmission conditions
- Generalized second order differential operators and their lateral conditions
- On the intrinsic form for second order differential operators
- On random walk simulation of one-dimensional diffusion processes with discontinuous coeffi\-cients
- On the constructions of the skew Brownian motion
- Some inverse Laplace transforms of exponential form
- Second order differential operators and Dirichlet integrals with singular coefficients. I: Functional calculus of one-dimensional operators
- Diffusion models for population dynamics incorporating individual behavior at boundaries: Applications to refuge design
- Three-dimensional modeling of mass transfer in porous media using the mixed hybrid finite elements and the random-walk methods
- Hitting, occupation and inverse local times of one-dimensional diffusions: Martingale and excursion approaches
- Modeling the diffusion of heat energy within composites of homogeneous materials using the uncertainty principle
- One-dimensional heat equation with discontinuous conductance
- An exponential timestepping algorithm for diffusion with discontinuous coefficients
- Simulating diffusion processes in discontinuous media: benchmark tests
- Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps
- Two Brownian particles with rank-based characteristics and skew-elastic collisions
- A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients
- Skew Ornstein-Uhlenbeck processes and their financial applications
- The general diffusion operator and positivity preserving semigroups in one dimension
- On second order differential operators
- Elementary Solutions for Certain Parabolic Partial Differential Equations
- Knotting of One-Dimensional Feller Processes
- A Note on a Laplace Transform Pair Associated with Mass Transport in Porous Media and Heat Transport Problems
- Asymptotic Behavior of Skew Conditional Heat Kernels on Graph Networks
- Exact simulation of one-dimensional stochastic differential equations involving the local time at zero of the unknown process
- Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics
- DENSITY OF SKEW BROWNIAN MOTION AND ITS FUNCTIONALS WITH APPLICATION IN FINANCE
- A Donsker theorem to simulate one-dimensional processes with measurable coefficients
- Bounds for the fundamental solution of a parabolic equation
- Exact Simulation of Brownian Diffusions with Drift Admitting Jumps
- Diffusion Processes in One Dimension