Results 51 to 60 of about 1,119 (105)

Inverse source problems for degenerate time-fractional PDE

, 2020
In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one involves a time ...
Al-Salti, Nasser, Karimov, Erkinjon
core  

Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces

, 2016
The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^\alpha$ with nonnegative initial data,
Xiao, Weiliang, Zhou, Xuhuan
core   +1 more source

On some inverse problems for a degenerate parabolic equation with involution

Open Mathematics
In this paper, the solvability of some initial-boundary value problems is considered for a nonlocal analogue of the degenerate parabolic equation. The inverse problems are studied for the case where it is necessary to find not only a solution to the ...
Turmetov Batirkhan, Shalkhar Ainur
doaj   +1 more source

On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise

Advances in Nonlinear Analysis, 2017
In this article, we deal with the stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasis is on analyzing the effects of a multiplicative Lévy noise on such problems and on establishing a well ...
Biswas Imran H., Majee Ananta K., Vallet Guy   +2 more
doaj   +1 more source

Schauder estimates on bounded domains for KFP operators with coefficients measurable in time and Hölder continuous in space

Analysis and Geometry in Metric Spaces
We consider degenerate Kolmogorov-Fokker-Planck operators ℒu=∑i,j=1qaij(x,t)uxixj+∑k,j=1Nbjkxkuxj−ut,{\mathcal{ {\mathcal L} }}u=\mathop{\sum }\limits_{i,j=1}^{q}{a}_{ij}\left(x,t){u}_{{x}_{i}{x}_{j}}+\mathop{\sum }\limits_{k,j=1}^{N}{b}_{jk}{x}_{k}{u}_{{
Biagi Stefano, Bramanti Marco
doaj   +1 more source

Near Field Asymptotic Behavior for the Porous Medium Equation on the Half-Line

Advanced Nonlinear Studies, 2017
Kamin and Vázquez [11] proved in 1991 that solutions to the Cauchy–Dirichlet problem for the porous medium equation ut=(um)x⁢x${u_{t}=(u^{m})_{xx}}$, m>1${m>1}$, on the half-line with zero boundary data and nonnegative compactly supported integrable ...
Cortázar Carmen, Quirós Fernando, Wolanski Noemi   +2 more
doaj   +1 more source

Inverse coefficient problem for Grushin-type parabolic operators

, 2013
The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators studied in this paper.
Beauchard, Karine, Cannarsa, Piermarco
core   +1 more source

On a class of fully nonlinear parabolic equations

Advances in Nonlinear Analysis, 2016
We study the homogeneous Dirichlet problem for the fully nonlinear ...
Antontsev Stanislav, Shmarev Sergey
doaj   +1 more source

Behavior of different numerical schemes for population genetic drift problems [PDF]

, 2016
In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation.
Chen, Minxin, Liu, Chun, Xu, Shixin, Yue, Xingye, Zhang, Ran   +4 more
core  

Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity

, 2014
In this paper, we establish a local gradient estimate for a $p$-Lpalacian equation with a fast growing gradient nonlinearity. With this estimate, we can prove a parabolic Liouville theorem for ancient solutions satisfying some growth restriction near ...
Attouchi, Amal
core   +1 more source