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We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…
We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
We develop of a field-theoretic approach for the treatment of both the non-local and the non-linear response of structured liquid dielectrics. Our systems of interest are composed of dipolar solvent molecules and simple salt cations and…
Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
Elliptic flow holds much promise for studying the early-time thermalization attained in ultrarelativistic nuclear collisions. Flow measurements also provide a means of distinguishing between hydrodynamic models and calculations which…
This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments…
We study the local behavior of the nodal sets of the solutions to elliptic quasilinear equations with nonlinear conductivity part, \begin{equation*} \operatorname{div}(A_s(x,u)\nabla u)=\operatorname{div}{\vec f}(x), \end{equation*} where…
We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of…
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…
We formulate the mapping between a large class of nonlinear wave equations and flow equations for barotropic fluid with internal surface tension and capillary effects. Motivated by statistical mechanics and multi-channel physics arguments,…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
There are few approaches to the solution of a system of nonlinear differential equations in partial derivatives, for example $\cite{NK87} - \cite{EK98}$. In our paper we propose an approach that was used to solve the Navier-Stokes equations…
We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. Under minimal structural assumptions on the graph, we…
We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving fluid interface in terms of a one-dimensional generating curve.…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
The way a relativistic system approaches fluid dynamical behaviour can be understood physically through the signals that will contribute to its linear response to perturbations. What these signals are is captured in the analytic structure…