Elliptic equations in $ \mathbb{R}^2 $ involving supercritical exponential growth by Yony Raúl Santaria Leuyacc

“…To show the existence of weak solutions, we used variational methods and a new type of the Trudinger-Moser inequality defined on the whole two-dimensional space.…”
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On the Incompressible Limit for the Compressible Flows of Liquid Crystals under Strong Stratification on Bounded Domains by Young-Sam Kwon

“…We study the incompressible limit of weak solutions for the compressible flows of liquid crystals under strong stratification on bounded domains.…”
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Micropolar Fluids with Vanishing Viscosity by E. Ortega-Torres, E. J. Villamizar-Roa, M. A. Rojas-Medar

“…A study of the convergence of weak solutions of the nonstationary micropolar fluids, in bounded domains of ℝ𝑛, when the viscosities tend to zero, is established. …”
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Incompressible Limit for the Compressible Flows of Nematic Liquid Crystals in the Whole Space by Young-Sam Kwon

“…We here study the incompressible limit of weak solutions of the compressible flows of nematic liquid crystals in the whole space R2.…”
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A Regularity Criterion for the 3D Incompressible Magnetohydrodynamics Equations in the Multiplier Spaces by Chunhong Tian

“…We are concerned with the regularity criterion for weak solutions to the 3D incompressible MHD equations in this paper. …”
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A boundary value problem for cold plasma dynamics by Thomas H. Otway

“…A weak Guderley-Morawetz problem is formulated for a mixed elliptic-hyperbolic system that arises in models of wave propagation in cold plasma. Weak solutions are shown to exist in a weighted Hilbert space. …”
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Navier-Stokes Equations with Potentials by Adriana-Ioana Lefter

“…Using the theory of nonlinear semigroups, we prove existence results for strong and weak solutions. Examples are also provided.…”
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On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary by Alexander Zlotnik

“…For global in time weak solutions having nonstrictly positive density, the linear in time two-sided bounds for the gas volume growth are established.…”
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Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions by Ciprian G. Gal, Mahamadi Warma

“…More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.…”
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Nontrivial Solutions of the Kirchhoff-Type Fractional p-Laplacian Dirichlet Problem by Taiyong Chen, Wenbin Liu, Hua Jin

“…By using the mountain pass theorem and the genus properties in the critical point theory, we get some new results on the existence and multiplicity of nontrivial weak solutions for such Dirichlet problem.…”
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The Well-Posedness of the Solutions Based on the L1 Initial Value Condition by Huashui Zhan, Zhen Zhou

“…If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions.…”
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Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space by Hyungjin Huh

“…The uniqueness of weak solutions is proved for the solution U∈L∞0,T; Ym+2ℝ.…”
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A Note on the Generalized Camassa-Holm Equation by Yun Wu, Ping Zhao

“…We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. …”
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Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities by Jamal H. Al-Smail, Salim A. Messaoudi, Ala A. Talahmeh

“…By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions.…”
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A New Topological Degree Theory for Perturbations of Demicontinuous Operators and Applications to Nonlinear Equations with Nonmonotone Nonlinearities by Teffera M. Asfaw

“…In addition, a new existence result is given concerning existence of weak solutions for nonlinear wave equation with nonmonotone nonlinearity.…”
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Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems by Jie Yang, Haibo Chen, Senli Liu

“…By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. …”
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Existence of Optimal Control for a Nonlinear-Viscous Fluid Model by Evgenii S. Baranovskii, Mikhail A. Artemov

“…For a given bounded set of admissible controls, we construct generalized (weak) solutions that minimize a given cost functional.…”
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On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable by Huashui Zhan

“…By this innovation, the stability of weak solutions is proved.…”
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Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic by Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini

“…We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. …”
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On a System of Equations of a Non-Newtonian Micropolar Fluid by G. M. de Araújo, M. A. F. de Araújo, E. F. L. Lucena

“…To prove the existence of weak solutions we use the method of Faedo-Galerkin and compactness arguments. …”
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