相关论文: Weak asymptotics method

We analyze systems of semilinear wave equations in $3+1$ dimensions whose associated asymptotic equation admit bounded solutions for suitably small choices of initial data. Under this special case of the weak null condition, which we refer…

We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…

In this paper we study a system of equations which appear in the modelling of many physical phenomena. Initially this system appeared in description of the large scale structure formation. Recently it is derived as a second order queueing…

We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…

We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…

The family of fifth order nonlinear evolution equations is studied. Some traveling wave elliptic solutions are found. The classification of these exact solutions is given.

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…

We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…

We investigate slowly converging solutions for non-linear evolution equations of elliptic or parabolic type. These equations arise from the study of isolated singularities in geometric variational problems. Slowly converging solutions have…

In this paper, we prove that the existence of globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking. We first introduce a new set of independent and dependent variables in…

The moving coframe method is applied to solve the local equivalence problem for the class of nonlinear wave equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…

In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations. Small amplitude waves are studied within the linearization approximation…

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations…

We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the domain interior and on the boundary. When the nonlinearities satisfy some monotonicity…

Stationary solutions asymptoting to nonlinear plane waves of the nonlinear Schr\"odinger equation with a PT-symmetric, complex linear potential are characterized. The potential includes both a spatially varying gain-loss profile and a…

We investigate a semilinear wave equation with energy-critical nonlinearity and a nonlinear damping mechanism driven by the total energy of the system. The model combines the quintic defocusing term with a time-dependent dissipation of the…

We develop mixed finite element methods for nonlinear reaction-diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations.…

In this work we developed a new problem solution methodology of contact interaction of acoustic medium with resilient finite bodies of cylindrical form, based on application of boundary integral equations method in conjunction with series…

In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to…