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Elliptic problems in generalized Orlicz-Musielak spaces

Piotr Gwiazda, Piotr Minakowski, Aneta Wróblewska-Kamińska (2012)

Open Mathematics

We consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.

Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces

Azeddine Aissaoui Fqayeh, Abdelmoujib Benkirane, Mostafa El Moumni (2014)

Applicationes Mathematicae

We discuss the existence of entropy solution for the strongly nonlinear unilateral parabolic inequalities associated to the nonlinear parabolic equations ∂u/∂t - div(a(x,t,u,∇u) + Φ(u)) + g(u)M(|∇u|) = μ in Q, in the framework of Orlicz-Sobolev spaces without any restriction on the N-function of the Orlicz spaces, where -div(a(x,t,u,∇u)) is a Leray-Lions operator and Φ ∈ C ⁰ ( ℝ , ℝ N ) . The function g(u)M(|∇u|) is a nonlinear lower order term with natural growth with respect to |∇u|, without satisfying the sign...

Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates

Igor Brilla (1990)

Aplikace matematiky

The paper deals with the analysis of generalized von Kármán equations which desribe stability of a thin circular viscoelastic clamped plate of constant thickness under a uniform compressible load which is applied along its edge and depends on a real parameter. The meaning of a solution of the mathematical problem is extended and various equivalent reformulations of the problem are considered. The structural pattern of the generalized von Kármán equations is analyzed from the point of view of nonlinear...

Exact solution of the time fractional variant Boussinesq-Burgers equations

Bibekananda Bira, Hemanta Mandal, Dia Zeidan (2021)

Applications of Mathematics

In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal groups of transformations containing some arbitrary constants. Next, we obtain the system of optimal algebras for the symmetry group of transformations. Afterward, we consider one of the optimal algebras and construct similarity variables, which reduces the given system of fractional partial differential equations (FPDEs) to fractional...

Existence for the stationary MHD-equations coupled to heat transfer with nonlocal radiation effects

Pierre-Étienne Druet (2009)

Czechoslovak Mathematical Journal

We consider the problem of influencing the motion of an electrically conducting fluid with an applied steady magnetic field. Since the flow is originating from buoyancy, heat transfer has to be included in the model. The stationary system of magnetohydrodynamics is considered, and an approximation of Boussinesq type is used to describe the buoyancy. The heat sources given by the dissipation of current and the viscous friction are not neglected in the fluid. The vessel containing the fluid is embedded...

Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

Sylwia Barnaś (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.

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