Results 41 to 50 of about 4,702,923 (209)

A singular perturbed problem with critical Sobolev exponent

Topological Methods in Nonlinear Analysis, 2021
This paper deals with the following nonlinear elliptic problem \begin{equation}\label{eq0.1} -\varepsilon^2\Delta u+\omega V(x)u=u^{p}+u^{2^{*}-1},\quad u> 0\quad\text{in}\ \R^N, \end{equation} where $\omega\in\R^{+}$, $N\geq 3$, $p\in (1,2^{*}-1)$ with $2^{*}={2N}/({N-2})$, $\varepsilon> 0$ is a small parameter and $V(x)$ is a given function ...
Mengyao Chen, Qi Li
openaire   +2 more sources

Stability of Viscous Three‐Dimensional Stratified Couette Flow via Dispersion and Mixing

Communications on Pure and Applied Mathematics, Volume 79, Issue 12, Page 2435-2490, December 2026.
ABSTRACT This article explores the stability of stratified Couette flow in the viscous 3d$3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves.
Michele Coti Zelati, Augusto Del Zotto, Klaus Widmayer   +2 more
wiley   +1 more source

Strongly indefinite systems with critical Sobolev exponents [PDF]

Transactions of the American Mathematical Society, 1998
We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.
MITIDIERI, ENZO, HULSHOF J, VAN DER VORST R.   +2 more
openaire   +4 more sources

Performance of a Mixed Least‐Squares Finite Element Formulation With Application in Poroelasticity

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT A mixed least‐squares finite element method (LSFEM), previously proposed for the theory of porous media (TPM), is further investigated in this work. Finite deformation of a fully saturated, incompressible solid–fluid binary system is studied using the LSFEM.
Manu Hegde, Alexander Schwarz, Joachim Bluhm, Jörg Schröder   +3 more
wiley   +1 more source

The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

Advances in Nonlinear Analysis, 2020
We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
doaj   +1 more source

On multiple solutions of the Neumann problem involving the critical Sobolev exponent

, 2004
We consider the Neumann problem involving the critical Sobolev exponent and a nonhomogeneous boundary condition. We establish the existence of two solutions.
Chabrowski, J. H.
core   +1 more source

Global Graph Surrogates and Neural Graph Elements for Computational Mechanics

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT Machine learning surrogates are increasingly used to accelerate physics‐based simulations by predicting full‐field responses at a fraction of the computational cost. In this contribution, we present two complementary graph‐based approaches for surrogate modelling in computational mechanics.
Rutwik Gulakala, Marcus Stoffel
wiley   +1 more source

Quantitative maximal L2$L^2$‐regularity for viscous Hamilton–Jacobi PDEs in 2D and Mean Field Games

Bulletin of the London Mathematical Society, Volume 58, Issue 11, November 2026.
Abstract We discuss quantitative Calderón–Zygmund estimates in W2,2$W^{2,2}$ for 2D viscous Hamilton–Jacobi equations with natural growth in the gradient. We apply the result to obtain the existence of classical solutions for stationary second‐order mean field games systems in 2D with (defocusing) coupling behaving like mα$m^\alpha$ for any α>0$\alpha >
Alessandro Goffi
wiley   +1 more source

Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

, 2012
In this paper, we show finite time blow-up of solutions of the p−wave equation in ℝN, with critical Sobolev exponent.
S. Ibrahim, A. Lyaghfouri
core   +1 more source

On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent

Communications on Pure and Applied Analysis
20 ...
Gu, Guangze, Jevnikar, Aleks
openaire   +2 more sources