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We present a brief review of methods based on the use of simpler solutions for constructing exact solutions of both nonlinear equations of mathematical physics and partial functional-differential equations. These methods are underlain by two general ideas: 1) simple exact solutions of the...
The development of the cryolithozone requires building and numerically implementing mathematical models of multiphysics thermoelastic processes involving with first-order phase transitions and occurring in the foundations of engineering structures and buildings. Numerical implementation of...
We consider the modulation instability of quasiharmonic longitudinal waves propagating in a homogeneous rod immersed in a nonlinearly elastic medium. The dynamic behavior of the rod is determined by the Mindlin–Herrmann theory, which refines the technical theory of rods. The accuracy of the...
We study the problem of a deformation of a straight strip bounded by an impermeable solid wall and a parallel free boundary. Three models of an incompressible fluid are considered: ideal fluid, classical viscous fluid, and dilute solution of a polymer. The influence of the viscous and...
We numerically simulate the Rayleigh–Taylor convection in a porous medium in the presence of initial density fluctuations at the interface between two fluid layers. We consider miscible fluids: the lower layer is composed of a single-component fluid medium, and the upper layer, of the same...
We discuss the stability problem for a boiling front moving at a constant speed in a porous permeable geothermal reservoir. We study the dispersion equation obtained by the method of normal modes. The decay of unstable small perturbations corresponding to large values of the dimensionless...
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