Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage by J. R. Fernández, M. Sofonea

“…We provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution of the model. We then introduce and study a fully discrete scheme for the numerical solutions of the problem. …”
Get full text

An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases by John R. Cannon, Daniel J. Galiffa

“…We ultimately show that a weak solution to the weak formulation of this model exists using a fixed point argument, which calls upon the construction of a weak formulation and the existence and uniqueness of an auxiliary problem.…”
Get full text

A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem by Teffera M. Asfaw

“…The theory is applied to prove existence of weak solution (s) for a nonlinear parabolic problem in appropriate Sobolev spaces.…”
Get full text

A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model by Aníbal Coronel, Luis Friz, Ian Hess, Alex Tello

“…In this note, we prove the existence and uniqueness of weak solutions for the boundary value problem modelling the stationary case of the bioconvective flow problem. …”
Get full text

Analysis of electroelastic frictionless contact problems with adhesion by Mircea Sofonea, Rachid Arhab, Raafat Tarraf

“…We provide variational formulations for the problems and prove the existence of a unique weak solution to each model. The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. …”
Get full text

On the frictionless unilateral contact of two viscoelastic bodies by M. Barboteu, T.-V. Hoarau-Mantel, M. Sofonea

“…We derive a variational formulation of the problem and prove the existence of a unique weak solution to the model by using arguments of evolution equations with maximal monotone operators. …”
Get full text

Nonlinear eigenvalue problems in Sobolev spaces with variable exponent by Teodora-Liliana Dinu

“…In the first case we show the existence of infinitely many weak solutions for any λ>0. In the second case we prove that if λ is large enough then there exists a nontrivial weak solution. …”
Get full text

Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory by Ahmed Hamidat, Hakim Bagua, Adel Aissaoui

“…We define a variational formulation for the model and demonstrate the existence of a single weak solution to the problem. The material behaviour is explained using a viscoelastic constitutive law that includes long-term memory and damage. …”
Get full text

A toxin-mediated size-structured population model: Finite difference approximation and well-posedness by Qihua Huang, Hao Wang

“…Existence-uniqueness of the weak solution to the model is established and convergence of the finite difference approximation to this unique solution is proved. …”
Get full text

A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme by Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis

“…Existence and uniqueness results are established and convergence of the finite difference approximation to the unique bounded variation weak solution of the model is obtained. Numerical simulations demonstrating the accuracy of the method are presented. …”
Get full text

Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, Pablo Alexei, Heid, Pascal, Süli, Endre

“…We prove that the weak solution, whose existence was already established in the literature, is unique, given some strengthened assumptions on the diffusive flux and the stress tensor, for small enough data. …”
Get full text

Simulation and Domain Identification of Sea Ice Thermodynamic System by Bing Tan, Peng Lu, Zhijun Li, Enmin Feng, Juan Wang

“…The unique existence of the weak solution of the thermodynamic system is proved. …”
Get full text

EARLY AND LATE STAGE PROFILES FOR A CHEMOTAXIS MODEL WITH DENSITY-DEPENDENT JUMP PROBABILITY by Tianyuan Xu, Shanming Ji, Chunhua Jin, Ming Mei, Jingxue Yin

“…The global convergence of the original weak solution to the steady state with exponential rate $O(e^{-ct})$ for some $c \gt 0$ is also obtained.…”
Get full text

Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries by Federica Di Michele, Bruno Rubino, Rosella Sampalmieri, Kateryna Stiepanova

“…The well posedness of the problem is ensured by adding a viscous term necessary for the convergence of the hybrid limit to an appropriate weak solution. Some numerical tests are also performed for different values of the viscous coefficient, in order to evaluate the effects of the viscosity, especially on the boundaries of the device.…”
Get full text

Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems by Teffera M. Asfaw

“…In the last section, an example is provided addressing existence of weak solution in X=Lp(0,T;W01,p(Ω)) of a nonlinear parabolic problem of the type ut-∑i=1n(∂/∂xi)ai(x,t,u,∇u)=f(x,t),  (x,t)∈Q; u(x,t)=0,  (x,t)∈∂Ω×(0,T); u(x,0)=0,  x∈Ω, where p>1, Ω is a nonempty, bounded, and open subset of RN, ai:Ω×(0,T)×R×RN→R  (i=1,2,…,n) satisfies certain growth conditions, and f∈Lp′(Q), Q=Ω×(0,T), and p′ is the conjugate exponent of p.…”
Get full text

Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities by Milena Dimova, Natalia Kolkovska, Nikolai Kutev

“…Two new necessary and sufficient conditions for blow up of the weak solutions are established. The first one addresses the blow up of the global weak solutions at infinity. …”
Get full text

Energy Conservation for 3D Tropical Climate Model in Periodic Domains by Hui Zhang

“…In this paper, we prove the energy conservation for the weak solutions of the 3D tropical climate model under some sufficient conditions. …”
Get full text

Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system by Ma, Dandan, Wu, Fan

“…This paper concerns the energy conservation for the weak solutions to the Navier–Stokes–Maxwell system. Although the Maxwell equation with hyperbolic nature, we still establish a $L^qL^p$ type condition guarantee validity of the energy equality for the weak solutions. …”
Get full text

Regularity for a Nonlinear Discontinuous Subelliptic System with Drift on the Heisenberg Group by Junli Zhang, Jialin Wang

“…In this paper, we prove the partial Hölder regularity of weak solutions and the partial Morrey regularity to horizontal gradients of weak solutions to a nonlinear discontinuous subelliptic system with drift on the Heisenberg group by the A-harmonic approximation, where the coefficients in the nonlinear subelliptic system are discontinuous and satisfy the VMO condition for x, ellipticity and growth condition with the growth index 1<p<2 for the Heisenberg gradient variable, and the nonhomogeneous terms satisfy the controllable growth condition and the natural growth condition, respectively.…”
Get full text

On the Boundary Value Condition of an Isotropic Parabolic Equation by Qitong Ou, Huashui Zhan

“…The well-posedness problem of anisotropic parabolic equation with variable exponents is studied in this paper. The weak solutions and the strong solutions are introduced, respectively. …”
Get full text