Conditions of boundary layer separation for Boussinesq equationsNonlinear Differential Equations and Applications NoDEA - Tập 30 - Trang 1-15 - 2023
Biyan Hu, Minxin Zhang, Hong Luo
In this paper, we analyze structural bifurcation of solutions to 2-D incompressible Boussinesq equations, where no-slip boundary condition for velocity and nonhomogenous Dirichlet boundary condition for temperature are considered. We get two conditions for boundary layer separation by Taylor expansion of the functions in Boussinesq equations and structural bifurcation theory for flows with Dirichl...... hiện toàn bộ
Higher differentiability for solutions of a general class of nonlinear elliptic obstacle problems with Orlicz growthNonlinear Differential Equations and Applications NoDEA - Tập 29 - Trang 1-25 - 2022
Sun-Sig Byun, Cho Namkyeong
In this paper we study a general class of nonlinear elliptic obstacle problems with Orlicz growth. Our purpose is to prove maximal differentiability of the gradient of solutions in the scale of both fractional Sobolev spaces and Besov spaces. Our regularity results extend the known higher differentiability results for such problems with polynomial growth to those with Orlicz growth.
Nonlinear diffusion equations driven by the p(·)-LaplacianNonlinear Differential Equations and Applications NoDEA - Tập 20 - Trang 37-64 - 2012
Goro Akagi, Kei Matsuura
This paper is concerned with nonlinear diffusion equations driven by the p(·)-Laplacian with variable exponents in space. The well-posedness is first checked for measurable exponents by setting up a subdifferential approach. The main purposes are to investigate the large-time behavior of solutions as well as to reveal the limiting behavior of solutions as p(·) diverges to the infinity in the whole...... hiện toàn bộ
Three-term spectral asymptotics for nonlinear Sturm-Liouville problemsNonlinear Differential Equations and Applications NoDEA - Tập 9 - Trang 239-254 - 2002
Tetsutaro Shibata
We consider the nonlinear Sturm-Liouville problem¶¶
$ -u''(t) + \vert u(t)\vert^{p-1}u(t) + f(u(t)) = \lambda u(t),\\ \enskip t \in I := (0, 1), \enskip u(0) = u(1) = 0, $
¶¶ where
$ p > 1 $
is a constant and
$ \lambda > 0 $
is an eigenvalue parameter. We establish the three-term asympto...... hiện toàn bộ
Semi-linear fractional $$\varvec{\sigma }$$ -evolution equations with mass or power non-linearityNonlinear Differential Equations and Applications NoDEA - Tập 25 - Trang 1-43 - 2018
Abdelatif Kainane Mezadek, Michael Reissig
In this paper we study the global (in time) existence of small data solutions to semi-linear fractional
$$\sigma $$
-evolution equations with mass or power non-linearity. Our main goal is to explain on the one hand the influence of the mass term and on the ot...... hiện toàn bộ