Results 1 to 10 of about 219 (45)
Existence of Solutions to the Poisson-Nernst-Planck System with Singular Permanent Charges in $\mathbb{R}^2$ [PDF]
SIAM Journal on Mathematical Analysis, 2021 In this paper, we study the well-posedness of Poisson–Nernst–Planck system with no-flux boundary condition and singular permanent charges in two dimension. The main difficulty comes from the lack of integrability of singular permanent charges.
C. Hsieh, Yongjiang Yu
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Properties of generalized degenerate parabolic systems
Advances in Nonlinear Analysis, 2022 In this article, we consider the parabolic system (ui)t=∇⋅(mUm−1A(∇ui,ui,x,t)+ℬ(ui,x,t)),(1≤i≤k){({u}^{i})}_{t}=\nabla \cdot (m{U}^{m-1}{\mathcal{A}}(\nabla {u}^{i},{u}^{i},x,t)+{\mathcal{ {\mathcal B} }}({u}^{i},x,t)),\hspace{1.0em}(1\le i\le k) in the ...
Kim Sunghoon, Lee Ki-Ahm
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Double-phase parabolic equations with variable growth and nonlinear sources
Advances in Nonlinear Analysis, 2022 We study the homogeneous Dirichlet problem for the parabolic equations ut−div(A(z,∣∇u∣)∇u)=F(z,u,∇u),z=(x,t)∈Ω×(0,T),{u}_{t}-{\rm{div}}\left({\mathcal{A}}\left(z,| \nabla u| )\nabla u)=F\left(z,u,\nabla u),\hspace{1.0em}z=\left(x,t)\in \Omega \times ...
Arora Rakesh, Shmarev Sergey
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On the dynamics of grounded shallow ice sheets: Modeling and analysis
Advances in Nonlinear Analysis, 2023 In this article, we formulate a model describing the evolution of thickness of a grounded shallow ice sheet. The thickness of the ice sheet is constrained to be nonnegative. This renders the problem under consideration an obstacle problem.
Piersanti Paolo, Temam Roger
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Nonlinear elliptic boundary value problems with convection term and Hardy potential
Moroccan Journal of Pure and Applied Analysis, 2023 In this paper, we deal with a nonlinear elliptic problems that incorporate a Hardy potential and a nonlinear convection term. We establish the existence and regularity of solutions under various assumptions concerning the summability of the source term f.
Achhoud Fessel +2 more
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On the second-order regularity of solutions to the parabolic p-Laplace equation [PDF]
, 2021 In this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that D(vertical bar Du vertical bar(p-2+s/2) Du) exists as a function and belongs to L-loc(2) with s ...
Feng, Yawen +2 more
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A nonlinear parabolic problem with singular terms and nonregular data [PDF]
, 2019 We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum, of the form $$ \begin{cases} \dys u_t - \Delta_p u = h(u)f ...
Oliva, Francescantonio +1 more
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Improved regularity for the stochastic fast diffusion equation
, 2023 We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter $m\in (0,1)$, with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative Wiener noise ...
Ciotir, Ioana +2 more
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Hölder continuity of singular parabolic equations with variable nonlinearity
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 In this paper we obtain the local Hölder regularity of the weak solutions for singular parabolic equations with variable exponents. The proof is based on DiBenedetto’s technique called intrinsic scaling; by choosing an appropriate geometry one can deduce
Bahja Hamid El
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On the role of kinetic and interfacial anisotropy in the crystal growth theory
, 2012 A planar anisotropic curvature flow equation with constant driving force term is considered when the interfacial energy is crystalline. The driving force term is given so that a closed convex set grows if it is sufficiently large.
M. Giga, Y. Giga
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