Z. Darbenas, R. van der Hout, and M. Oliver,
Conditional uniqueness of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit,
submitted for publication.
H. Mohamad and M. Oliver,
High-order uniformly accurate time integrators for semilinear wave
equations of Klein-Gordon type in the non-relativistic limit,
submitted for publication.
M. Oliver and S. Vasylkevych,
A new construction of modified equations for
variational integrators,
submitted for publication.
M. Oliver and S. Vasylkevych,
Non-negative matrix factorization with factorizable feature matrix,
submitted for publication.
Z. Darbenas, R. van der Hout, and M. Oliver,
Long-time asymptotics of solutions to the Keller-Rubinow model
for Liesegang rings in the fast reaction limit,
Ann. Inst. H. Poincaré Anal. Non Linéaire (2022), online
first, doi:10.4171/AIHPC/34.
H. Mohamad and M. Oliver,
Numerical integration of functions of a rapidly rotating
phase,
SIAM J. Num. Anal. 59 (2021), 2310-2319.
G. Özden and M. Oliver,
Variational balance models for the three-dimensional
Euler-Boussinesq equations with full Coriolis force,
Phys. Fluids 33 (2021), 076606.
Z. Darbenas and M. Oliver,
Breakdown of Liesegang precipitation bands
in a simplified fast reaction limit of the Keller-Rubinow model,
Nonlinear Differ. Equ. Appl. 28 (2021), 4, doi:10.1007/s00030-020-00663-7.
S. Juricke, S. Danilov, N. Koldunov, M. Oliver, D.V. Sein,
D. Sidorenko, and Q. Wang,
A kinematic kinetic energy backscatter parametrization: From implementation to global ocean simulations,
J. Adv. Model. Earth Syst. 12 (2020), e2020MS002175, doi:10.1029/2020MS002175.
G.T. Masur and M. Oliver,
Optimal balance for rotating shallow water in
primitive variables,
Geophys. Astrophys. Fluid Dyn. 114 (2020), 429-452.
I. Akramov and M. Oliver,
On the existence of solutions to a bi-planar Monge-Ampère equation,
Acta Math. Sci. 40 (2020), 379-388.
S. Juricke, S. Danilov, N. Koldunov, M. Oliver, and D. Sidorenko,
Ocean kinetic energy backscatter parametrization on unstructured grids: Impact on global eddy-permitting simulations,
J. Adv. Model. Earth Syst. 12 (2020),
e2019MS001855, doi:10.1029/2019MS001855.
Z. Darbenas and M. Oliver,
Uniqueness of solutions for weakly degenerate cordial Volterra
integral equations,
J. Integral Equ. Appl. 31 (2019), 307-327,
doi:10.1216/JIE-2019-31-3-307.
M. Oliver and S. Vasylkevych,
Geodesic motion on groups of diffeomorphisms with H^{1} metric as geometric generalised Lagrangian mean theory,
Geophys. Astrophys. Fluid Dyn. 113 (2019), 466-490.
S. Juricke, S. Danilov, A. Kutsenko, and M. Oliver,
Ocean kinetic energy backscatter parametrizations on unstructured
grids: Impact on mesoscale turbulence in a channel,
Ocean Model. 138 (2019), 51-67, doi:10.1016/j.ocemod.2019.03.009.
H. Mohamad and M. Oliver,
A direct construction of a slow manifold for
a semilinear wave equation of Klein-Gordon type,
J. Differential Equations 267 (2019), 1-14, doi:10.1016/j.jde.2019.01.001.
C.L.E. Franzke, M. Oliver, J.D.M. Rademacher, and G. Badin,
Multi-scale methods for geophysical flows,
in: C. Eden and A. Iske, eds.,
"Energy Transfers in Atmosphere and Ocean", pp. 1-51, Springer-Verlag, 2019.
J.-S. von Storch, G. Badin, and M. Oliver,
The interior energy pathway: inertial gravity wave emission by
oceanic flows,
in: C. Eden and A. Iske, eds.,
"Energy Transfers in Atmosphere and Ocean", pp. 53-85, Springer-Verlag, 2019.
S. Danilov, S. Juricke, A. Kutsenko, and M. Oliver,
Toward consistent subgrid momentum closures in ocean models,
in: C. Eden and A. Iske, eds.,
"Energy Transfers in Atmosphere and Ocean", pp. 145-192, Springer-Verlag, 2019.
M. Oliver,
An estimate on the Bedrosian commutator in Sobolev space,
J. Inequal. Appl. 2018 (2018), 348, doi:10.1186/s13660-018-1940-3.
G. Badin, M. Oliver, and S. Vasylkevych,
Geometric Lagrangian averaged Euler-Boussinesq and primitive equations,
J. Phys. A: Math. Theor. 51 (2018), 455501, doi:10.1088/1751-8121/aae1cb.
H. Mohamad and M. Oliver,
H^{s}-class construction of an almost invariant slow subspace
for the Klein-Gordon equation in the non-relativistic limit,
J. Math. Phys. 59 (2018), 051509.
G.A. Gottwald, H. Mohamad, and M. Oliver,
Optimal balance via adiabatic invariance of approximate slow
manifolds,
Multiscale Model. Simul. 15 (2017), 1404-1422.
M. Oliver,
Lagrangian averaging with geodesic mean,
Proc. R. Soc. Lond. A 473 (2017), 20170558.
D.G. Dritschel, G.A. Gottwald, and M. Oliver,
Comparison of variational balance models for the rotating shallow water equations,
J. Fluid Mech. 822 (2017), 689-716.
C. Wulff and M. Oliver,
Exponentially accurate Hamiltonian embeddings of symplectic A-stable
Runge-Kutta methods for Hamiltonian semilinear evolution equations,
P. Roy. Soc. Edinb. 146A (2016), 1265-1301.
M. Oliver and S. Vasylkevych,
Generalized large-scale semigeostrophic approximations for the
f-plane primitive equations,
J. Phys. A: Math. Theor. 49 (2016), 184001.
A. Merico, G. Brandt, S.L. Smith, and M. Oliver,
Sustaining diversity in trait-based models of phytoplankton communities,
Front. Ecol. Evol. 2 (2014),
59, doi:10.3389/fevo.2014.00059.
G. Gottwald and M. Oliver,
Slow dynamics via degenerate variational
asymptotics,
Proc. R. Soc. Lond. A 470 (2014), 20140460,
doi:10.1098/rspa.2014.0460.
M. Oliver,
A variational derivation of the geostrophic momentum approximation,
J. Fluid Mech. 751 (2014), R2, doi:10.1017/jfm.2014.309.
M. Oliver and C. Wulff,
Stability under Galerkin truncation of
A-stable Runge-Kutta discretizations in time,
P. Roy. Soc. Edinb. A 144 (2014), 603-636.
O. Bokhove, V. Molchanov, M. Oliver, and B. Peeters,
On the rate of convergence of the
Hamiltonian particle-mesh method,
in: Meshfree Methods for Partial Differential Equations VI (M. Griebel
and M.A. Schweitzer, eds.),
Lecture Notes in Computational Science and Engineering Vol. 89,
Springer, Berlin, 2013, pp. 25-43.
M. Çalık, M. Oliver, and S. Vasylkevych,
Global well-posedness for the
generalized large-scale semigeostrophic equations,
Arch. Ration. Mech. An. 207 (2013), 969-990.
M. Çalık and M. Oliver,
Weak solutions for generalized large-scale
semigeostrophic equations,
Commun. Pure Appl. Ana. 12 (2013), 939-955.
V. Molchanov and M. Oliver,
Convergence of the Hamiltonian
particle-mesh method for barotropic fluid flow,
Math. Comp. 82 (2013), 861-891.
M. Oliver and S. Vasylkevych,
Generalized LSG models with varying
Coriolis parameter,
Geophys. Astrophys. Fluid Dyn. 107 (2013), 259-276.
M. Oliver and C. Wulff,
A-stable Runge-Kutta methods for semilinear
evolution equations,
J. Functional Anal. 263 (2012), 1981-2023.
R.M. Kerr and M. Oliver,
The ever-elusive blowup in the mathematical description of
fluids,
in: "An Invitation to Mathematics: From Competitions to Research,"
D. Schleicher and M. Lackmann (eds.), pp. 137-164,
Springer-Verlag, Berlin, 2011.
Also published in German as: Regulär oder nicht regulär?
Strömungssingularitäten auf der Spur,
in: "Eine Einladung in die Mathematik,"
D. Schleicher and M. Lackmann (eds.), pp. 141-170,
Springer-Verlag, Berlin, 2013.
M. Oliver and S. Vasylkevych,
Hamiltonian formalism for models of
rotating shallow water in semigeostrophic scaling,
Discret. Contin. Dyn. S. 31 (2011), 827-846.
G. Gottwald and M. Oliver,
Boltzmann's dilemma: an
introduction to statistical mechanics via the Kac ring,
SIAM Rev. 51 (2009), 613-635.
O. Bokhove and M. Oliver,
A parcel formulation for Hamiltonian layer
models,
Geophys. Astrophys. Fluid Dyn. 103 (2009),
423-442.
M. Oliver and O. Bühler,
Transparent boundary conditions as
dissipative subgrid closures for
the spectral representation of scalar advection by shear flows,
J. Math. Phys. 48 (2007), 065502, 26 pp.
G. Gottwald, M. Oliver, and N. Tecu,
Long-time accuracy for approximate slow
manifolds in a finite dimensional model of balance,
J. Nonlinear Sci. 17 (2007), 283-307.
O. Bokhove and M. Oliver,
Parcel Eulerian-Lagrangian fluid dynamics of
rotating geophysical flows,
Proc. R. Soc. Lond. A 462 (2006), 2563-2573.
M. Oliver,
Variational asymptotics for rotating shallow
water near geostrophy: A
transformational approach,
J. Fluid Mech. 551 (2006), 197-234.
N.D. Aparicio, S.J.A. Malham, and M. Oliver,
Numerical evaluation of the Evans function by Magnus
integration,
BIT Numerical Mathematics 45 (2005), 219-258.
M. Oliver, M. West, and C. Wulff,
Approximate momentum conservation for spatial
semidiscretizations of nonlinear wave equations,
Numerische Mathematik 97 (2004), 493-535.
R. Ford, S.J.A. Malham, and M. Oliver,
A new model for shallow water in the low Rossby-number limit,
J. Fluid Mech. 450 (2002), 287-296.
M. Oliver,
The Lagrangian averaged Euler equations as the short-time inviscid
limit of the Navier--Stokes equations with Besov class data in
R^{2},
Commun. Pure Appl. Ana. 1 (2002), 221-235.
M. Oliver and E.S. Titi,
On the domain of analyticity for solutions of second
order analytic nonlinear differential equations,
J. Differential Equations 174 (2001), 55-74.
M. Oliver and S. Shkoller,
The vortex blob method as a second-grade non-Newtonian fluid,
Comm. Partial Differential Equations 26 (2001), 295-314.
M. Oliver and S. Malham,
Accelerating fronts in autocatalysis,
Proc. R. Soc. Lond. A 456 (2000), 1609-1624.
M. Oliver and E.S. Titi,
Gevrey regularity for the attractor of a partially
dissipative model of Bénard convection in a
porous medium,
J. Differential Equations 163 (2000), 292-311.
S. Kouranbaeva and M. Oliver,
Global Well-Posedness for the Averaged Euler Equations in Two
Dimensions,
Phys. D 138 (2000), 197-209.
M. Oliver and E.S. Titi,
Remark on the rate of decay of higher order derivatives
for solutions to the Navier-Stokes equations in
R^{n},
J. Funct. Anal. 172 (2000), 1-18.
M. Oliver and E.S. Titi,
Analyticity of the attractor and the number of
determining nodes for a weakly damped driven nonlinear
Schrödinger Equation,
Indiana Univ. Math. J. 47 (1998), 49-74.
M. Oliver,
Justification of the shallow water limit for a rigid lid
flow with bottom topography,
Theoretical and Computational Fluid Dynamics 9
(1997), 311-324.
M. Oliver,
Classical solutions for a generalized Euler equation in
two dimensions,
J. Math. Anal. Appl. 215 (1997), 471-484.
C.D. Levermore and M. Oliver,
Analyticity of solutions for a generalized Euler
equation,
J. Differential Equations 133 (1997), 321-339.
C.D. Levermore and M. Oliver,
Distribution-valued initial data for the complex
Ginzburg-Landau equation,
Comm. Partial Differential Equations 22 (1997), 39-48.
M. Oliver,
Shallow Water Models: Well-posedness, Regularity,
and Justification,
in ``Proceedings of the 15th IMACS World
Congress on Scientific Computation, Modelling and Applied
Mathematics, Berlin, August 1997,'' Vol. 3, pp. 295-300,
Verlag Wissenschaft & Technik, Berlin, 1997.
C.D. Levermore, M. Oliver, and E.S. Titi,
Global well-posedness for models of shallow water in a
basin with a varying bottom,
Indiana Univ. Math. J. 45 (1996), 479-510.
C.D. Levermore, M. Oliver, and E.S. Titi,
Global Well-Posedness for the Lake Equations,
Physica D 98 (1996), 492-509.
C.D. Levermore and M. Oliver,
The complex Ginzburg-Landau equation as a model problem,
in "Lectures in Applied Mathematics," Vol. 31, pp. 141-190,
AMS, Providence, Rhode Island, 1996.
M. Bartuccelli, J.D. Gibbon, and M. Oliver,
Length scales in solutions of the complex
Ginzburg-Landau equation,
Physica D 89 (1996), 267-286.
M. Oliver,
A Mathematical Investigation of Models of
Shallow Water with a Varying Bottom,
Ph.D. dissertation,
University of Arizona, Tucson, Arizona, 1996.
M. Oliver,
Attractors, Regularity and Length Scales in the
Complex Ginzburg-Landau Equation with a Nonlinearity
of Arbitrary Order,
Diplomarbeit, WWU Münster and Imperial College, London, 1992.