Rothe time-discretization method for a nonlocal problem arising in thermoelasticity

Rothe Time-discretization Method Applied to a Quasilinear Wave Equation Subject to Integral Conditions

Recently, the study of initial-boundary value problems for hyperbolic equations with boundary integral conditions has received considerable attention. This kind of conditions has many important applications. For instance, they appear in the case where a direct measurement quantity is impossible; however, their mean values are known. In this paper, we deal with a class of quasilinear hyperbolic ...

A Time Discretization Scheme for a Nonlocal Degenerate Problem Modelling Resistance Spot Welding

In the current work we construct a nonlocal mathematical model describing the phase transition occurs during the resistance spot welding process in the industry of metallurgy. We then consider a time discretization scheme for solving the resulting nonlocal moving boundary problem. The scheme consists of solving at each time step a linear elliptic partial differential equation and then making a ...

A Nonlocal Quenching Problem Arising in Micro-electro Mechanical System

In this paper, we study a nonlocal parabolic problem arising in the study of microelectro mechanical system. The nonlocal nonlinearity involved is related to an integral over the spatial domain. We first give the structure of stationary solutions. Then we derive the convergence of global (in time) solution to the maximal solution as the time tends to infinity. Finally, we provide some quenching...

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data

Method of Rothe for a Hyperbolic