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 initial‐boundary value problems for a Sobolev equation with exponential nonlinearities,
classical, and nonclassical boundary conditions are considered. For this model, which …

The initial‐boundary value problem for an equation of ion sound waves in plasma is
considered. A theorem on nonextendable solution is proved. The blow‐up phenomena are …

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 consider a series of initial-boundary value problems for the equation of ion-sound waves
in a plasma. For each of them we prove the local (in time) solubility and perform an …

The initial boundary-value problem for the equation of ion-sound waves in a plasma is
studied. A theorem on the nonextendable solution is proved. Sufficient conditions for the …

A new approach to the numerical simulation of the reaction front motion in a nonlinear
singularly perturbed partial differential equation of the reaction–diffusion type is proposed. It …

Рассмотрена серия начально-краевых задач для уравнения ионно-звуковых волн в
плазме. Для каждой из них доказана локальная (по времени) разрешимость и …

Рассмотрена начально-краевая задача для уравнения ионно-звуковых волн в плазме.
При этом распределение Больцмана плотности электронов приближено квадратичной …