Unilateral Problem for a Viscoelastic Beam Equation Type p-Laplacian with Strong Damping and Logarithmic Source

In this manuscript, we investigate the unilateral problem for a viscoelastic beam equation of p-Laplacian type. The competition of the strong damping versus the logarithmic source term is considered. We use the potential well theory. Taking into account the initial data is in the stability set created by the Nehari surface, we prove the existence and uniqueness of global solutions by using the penalization method and Faedo-Galerkin’s approximation.

On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space

PurposeIn the present paper, the authors will discuss the solvability of a class of nonlinear anisotropic elliptic problems (P), with the presence of a lower-order term and a non-polynomial growth which does not satisfy any sign condition which is described by an N-uplet of N-functions satisfying the Δ2-condition, within the fulfilling of anisotropic Sobolev-Orlicz space. In addition, the resulting analysis requires the development of some new aspects of the theory in this field. The source term is merely integrable.Design/methodology/approachAn approximation procedure and some priori estimates are used to solve the problem.FindingsThe authors prove the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain. The resulting analysis requires the development of some new aspects of the theory in this field.Originality/valueTo the best of the authors’ knowledge, this is the first paper that investigates the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain.

On a class of nonlinear elliptic problems with obstacle

This paper deals with the existence and regularity of some unilateral problem associated to a nonlinear equation of type {-\operatorname{div}(a(x,u,\nabla u))+H(x,u,\nabla u)=f}.

Existence of Solutions for Some Nonlinear Elliptic Anisotropic Unilateral Problems with Lower Order Terms

In this paper, we prove the existence of entropy solutions for anisotropic elliptic unilateral problem associated to the equations of the form$$ - \sum\limits_{i = 1}^N {{\partial _i}{a_i}(x,u,\nabla u) - } \sum\limits_{i = 1}^N {{\partial _i}{\phi _i}(u) = f,} $$where the right hand side f belongs to L1(Ω). The operator $- \sum\nolimits_{i = 1}^N {{\partial _i}{a_i}\left( {x,u,\nabla u} \right)} $ is a Leray-Lions anisotropic operator and ϕi ∈ C0(ℝ,ℝ).

Dynamic contact of a thermoelastic Mindlin–Timoshenko beam with a rigid obstacle

We concentrate on the dynamics of a thermoelastic Mindlin–Timoshenko beam striking a rigid obstacle. We state classical formulations involving complementarity conditions. Weak formulations are in the form of systems consisting of a hyperbolic variational inequality for a deflection, a hyperbolic and a parabolic equation for an angle of rotation and a thermal strain, respectively. The penalization method is applied to solve the unilateral problem. The time derivative of the function representing the deflection of the beam’s middle line is not continuous due to the hitting the obstacle. The acceleration term has the form of a vector measure.

Study on the Assemble Interpretation Method of Inter Well Tracer Test

At present, test interpretation technology is still based on the rule and theory during 1960s-1980s, which wasn’t be developed and improved further in view of the new problems in field. The field practice and theory comparison have shown that these basic theory and interpretation model diverges obviously appropriate category, and have the singlet, unilateral problem of considered element, which can’t adapt to the quantification description of complex filtrate in porous medium. The basic theory and mathematic model of tracer test interpretation need to develop further, and interpretation means needs to improve corroboratively. From the point of numerical mathematics, the independent variables in reservoirs were found out and the objective function was constructed. Making use of improved real-number-style inheritance-arithmetic, the unitary parameters inversion and interpretation were accomplished in inter well tracer test.