We consider the Cauchy problem for a model partial differential equation of order three with
a non-linearity of the form $|\nabla u|^ q $. We prove that when $ q\in (1, 3/2] $ the Cauchy …

Three nonlinear equations for ion acoustic and drift waves in a plasma are derived. The
fundamental solution of the common linear part of the resulting nonlinear equations is …

§ 1. Введение Впервые явление полного разрушения (“complete blow-up”) было
обнаружено для уравнения−∆ u=| x|− 2u2, u⩾ 0, x∈ Ω\{0}⊂ RN,(1.1) в работе Х. Брезиса …

В работе рассмотрена абстрактная задача Коши с нелинейными операторными
коэффициентами. Доказано существование единственного непродолжаемого …

We consider two model non-linear equations describing electric oscillations in systems with
distributed parameters on the basis of diodes with non-linear characteristics. We obtain …

We consider an abstract Cauchy problem with non-linear operator coefficients and prove the
existence of a unique non-extendable classical solution. Under certain sufficient close-to …

An analytical-numerical approach is used to study the finite-time blow-up of the solution to
the initial boundary-value problem for the nonlinear Klein–Gordon equation. An analytical …

При рассмотрении так называемых цепных LC-линий передач на основе
полупроводниковых диодов–стабилитронов, варикапов с нелинейными …

New high-order nonlinear equations of the Sobolev type describing ion-sound plasma
waves in an external electric or magnetic field are derived. Despite the cumbersome form of …

An initial-boundary value problem for the multidimensional equation of ion-sound waves in a
plasma is considered. Its time-local solvability in the classical sense in Hölder spaces is …