scholarly journals A non-autonomous bifurcation problem for a non-local scalar one-dimensional parabolic equation

2020 ◽  
Vol 19 (11) ◽  
pp. 5181-5196
Author(s):  
Yanan Li ◽  
◽  
Alexandre N. Carvalho ◽  
Tito L. M. Luna ◽  
Estefani M. Moreira ◽  
...  
Keyword(s):  
Parabolic Equation ◽  
Bifurcation Problem ◽  
One Dimensional ◽  
Non Local

scholarly journals A locally one-dimensional scheme for a general parabolic equation describing microphysical processes in convective clouds

2021 ◽  
Vol 21 (4) ◽  
pp. 45-55
Author(s):  
B.A. Ashabokov ◽  
◽  
A.Kh. Khibiev ◽  
M.Kh. Shkhanukov-Lafishev ◽  
◽  
...  
Keyword(s):  
Parabolic Equation ◽  
Difference Scheme ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate ◽  
One Dimensional ◽  
Convective Clouds ◽  
Non Local ◽  
Microphysical Processes

A locally one-dimensional difference scheme for a general parabolic equation in a p-dimensional parallelepiped is considered. To describe microphysical processes in convective clouds, non-local (nonlinear) integral sources of a special type are included in the equation under consideration. An a priori estimate for the solution of a locally one-dimensional scheme is obtained and its convergence is proved.

Global solvability to the non-local problem for parabolic equation

2018 ◽  
Vol 2018 (1) ◽  
pp. 161-166
Author(s):  
J.O. Takhirov ◽  
Keyword(s):  
Parabolic Equation ◽  
Global Solvability ◽  
Local Problem ◽  
Non Local

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional case

2002 ◽  
Vol 54 (3) ◽  
pp. 331-346 ◽  
Author(s):  
Jacob Fish ◽  
Wen Chen ◽  
Gakuji Nagai
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Dimensional Case ◽  
One Dimensional ◽  
Dispersive Model ◽  
Non Local

Description of a one-dimensional vibrational state with a parabolic equation

1985 ◽  
Vol 21 (3) ◽  
pp. 297-301 ◽  
Author(s):  
A. K. Belyaev
Keyword(s):  
Parabolic Equation ◽  
Vibrational State ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document