In this paper, we consider the Cauchy problem for one nonclassical, third‐order, model
partial differential equation with nonlinearity| u| q in. We show that for q∈(1, 3], there are no …

The work continues a series of articles devoted to the peculiarities of solving coefficient
inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion …

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 …

We first consider the damped wave inequality∂ 2 u∂ t 2−∂ 2 u∂ x 2+∂ u∂ t≥ x σ| u| p, t>
0, x∈(0, L), where L> 0, σ∈ R, and p> 1, under the Dirichlet boundary conditions (u (t, 0), u …

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 …