Suchergebnisse

"In this paper we study the process of bilateral contact with adhesion and friction between a piezoelectric body and an insulator obstacle, the socalled foundation. The material's behavior is assumed to be electro-viscoelastic- viscoplastic; the process is quasistatic, the contact is modeled by a general non-local friction law with adhesion. The adhesion process is modeled by a bonding field on the contact surface. We derive a variational formulation for the problem and then, under a smallness assumption on the coe cient of friction, we prove the existence of a unique weak solution to the model. The proofs are based on a general results on elliptic variational inequalities and fixed point arguments."

"In this paper we consider an n-dimensional thermoelastic system, in a bounded domain, where the memory-type damping is acting on a part of the boundary and where the resolvent kernel k of ${-g^{\prime }(t)}/{g(0)} $ satisfies\linebreak $k^{\prime \prime }(t)\geq \gamma \left( t\right) (-k^{\prime }(t))^{p}$, $t\geq 0$, $1< p<\frac{3}{2} $. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. This work generalizes and improves earlier results in the literature."

We consider a mathematical model which describes the dynamic pro- cess of contact between a piezoelectric body and an electrically conductive foun- dation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law with thermal e ects. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear rst order evolution inequali- ties, the equations with monotone operators, and the xed point arguments.

"The paper deals with a nonlinear elasticity system with nonconstant coe cients. The existence and uniqueness of the solution of Neumann's problem is proved using Galerkin techniques and monotone operator theory, in Sobolev spaces with variable exponents."

"In this paper we consider the dynamic system for Bingham fluid in a three-dimensional thin domain with Fourier and Tresca boundary condition. We study the existence and uniqueness results for the weak solution, then we establish its asymptotic behavior, when the depth of the thin domain tends to zero. This study yields a mechanical laws that give a new description of the behavior this system."

In this paper, we consider a system of nonlinear viscoelastic wave equations with degenerate damping and source terms. We prove, with positive initial energy, the global nonexistence of solution by concavity method.

"In this paper, we consider a nonlinear $p-$Kirchhoff type hyperbolic equation with damping and source terms $$u_{tt}-M\left( \underset{\Omega }{\int }\left\vert \nabla u\right\vert ^{p}dx\right) \Delta _{p}u+\left\vert u_{t}\right\vert ^{m-2}u_{t}=\left\vert u\right\vert ^{r-2}u.$$ Under suitable assumptions and positive initial energy, we prove the global existence of solution by using the potential energy and Nehari's functionals. Finally, the stability of equation is established based on Komornik's integral inequality."

"The purpose of this work is to establish an extension of a Leggett- Williams type expansion-compression fixed point theorem for a sum of two operators. As illustration, our approach is applied to prove the existence of non trivial nonnegative solutions for two-point BVPs and three-point BVPs."

In this work, we use index xed point theory for perturbation of expan- sive mappings by l-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear di erential equation on the positive half-line. The nonlin- earity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave di erently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main results is given.

"The purpose of this work is to establish a new generalized form of the Krasnoselskii type compression-expansion fixed point theorem for a sum of an expansive operator and a completely continuous one. Applications to three non- linear boundary value problems associated to second order differential equations of coincidence type are included to illustrate the main results."

This report deals with a blow-up of the solutions to a class of semilinear parabolic equations with variable exponents nonlinearities. Under some appropriate assumptions on the given data, a more general lower bound for a blow-up time is obtained if the solutions blow up. This result extends the recent results given by Baghaei Khadijeh et al. \cite{Baghaei}, which ensures the lower bounds for the blow-up time of solutions with initial data $\varphi\left( 0\right) =\int_{\Omega }u_{0}{}^{k}dx$, $k$ = constant.

"This paper deals with a boundary value problem for a nonlinear differential equation with two conformable fractional derivatives and integral boundary conditions. The results of existence, uniqueness and stability of positive solutions are proved by using the Banach contraction principle, Guo-Krasnoselskii's fixed point theorem and Hyers-Ulam type stability. Two concrete examples are given to illustrate the main results."

"In this work, we are concerned with a problem of a logarithmic nonlinear wave equation with time-varying delay term. We established the local existence result and we proved a blow up result for the solution with negative initial energy under suitable conditions. This improves earlier results in the literature [11] for time-varying delay."