 Dear colleagues, the term of my presentation is instability of the contact discontinuity in the presence of density in homogenities. The main goals of my presentation is the study of the interface evolution between the two semi-infinite colliding mediums in the presence of density in homogenities, the study of nonlinear interactions and comparison of numerical and theoretical results. In the paper of Willikovic, it's noticed that in such case, the interface is unstable. And this type of instability is named Riksmail Mishkov-like instability. But no analysis is given. Following the paper of Berning and Rubenchuk, we analyzed the development of hydrodynamic instability at the interface in the nonlinear approximations up to the third order corrections to hydrodynamic quantities. Consider the problem statement. The impactor collides with the target. Velocity of the colliding is order of kilometers per second. Interface is flat and density in homogenities locate in impactor at initial. In homogenities is of harmonic type and characterized by the angle between wave vector k0 and x axis. This axis normal to unperturbed shock front. For the reason of high velocity, the elastoplastic properties of can be neglected and probably can be described by the equations of hydrodynamic. There are two shock waves in impactor and in target propagating from contact discontinuity in opposite directions. In addition to hydrodynamic equations, we can see the ranking Higonew conditions on shock waves 1 and 2 and boundary conditions on contact discontinuity. Equation of state in migranizing form is used to describe material behavior. In linear linear approximation, solution for hydrodynamic equations can be represented by a set of entropy vortex and sound waves. Entropy vortex wave move with environment velocity and in other words entropy vortex wave is frozen in environment. In the other hand, sound wave move with speed of sound and sound wave can be reflected and reflected on contact discontinuity. Reflected sound wave interact with shock wave in target that results in the formation of new sound and entropy vortex waves. Reflected sound wave also interacts with shock wave in impactor and that results in formation of new sound and entropy vortex wave and so on. It's important to know that only set of entropy vortex waves provide instability of contact discontinuity and sound waves cause only oscillations. In our previous work, we have shown that there is the region of initial angle, set 0 for which the solution includes only entropy vortex waves in shock area of impactor. This theoretical result is confirmed by direct numerical simulations. This figure corresponds to calculation with sound waves are present in target and in impactor and this figure corresponds to the calculation when sound wave present only limited area behind shock front of in impactor. In what force we choose this region for simplicity of our theoretical analysis. The results of linear analysis is that spike and bubble velocity are equal and constant in time. But as for now, linear analysis is not enough for correct description of instability development. Considering quadratic corrections, we use hydrodynamic equations, boundary conditions on contact discontinuity and results of linear analysis. As a result, we obtain the quadratic corrections to x velocity of contact discontinuity is linearly proportional to the time. And therefore, the model of quadratic corrections to constant contact discontinuity velocity and velocity itself increases infinitely with time. This fact is not observed in our numerical calculations. That's why we take into account cubic corrections. As a result of similar analysis, we obtained the cubic correction to x velocity of contact discontinuity is quadratically proportional to the time. Finally, the expression for contact discontinuity velocity, constant discontinuity x and x velocity is given by the formula. The presence of correction proportional to the time squared can provide, but not necessarily, the point of extremum. Following the work of burning interbenchic, we name this point as saturation point of growth. At the saturation time moment, the growth velocity is considered constant. In addition, analysis of poet's collision is carried out numerically. The statement of the problem is schematically presented in the figure, impactor, target and initial parameters can be represented here. On this slide, we present density profiles for sequential time moments demonstrating instability development, including later nonlinear stages. Firstly, we note that spike and bubble growth are different. This result can be obtained in two linear analysis. Secondly, the direction of growth spike and bubble is correlated with strip-like initial inhomogenities. The theoretical analysis up to the third order gives four dependencies for bubble and spike velocities. It's clear that bubble saturation time can be defined uniquely, point of extremum. See that right line or left figure at this point. Comparing the theoretical and numerical bubble position, one can see that good agreement is reached, theoretical straight line and numerical dashed line. In opposite to that, spike saturation time is undefendable. Because the extremum point lies out of the physical time range. For example, we tried two values for spike saturation time at compare theoretical spike position with the numerical one, one saturation time point and second. One can observe that there is good agreement only for early stage of the instability development. The question about spike saturation remains to be opened. Next, we want to compare a new type of instability with the classical instability. There too, we set density inhomogenities in impact in tessellite-like mode in order to make instability development symmetric. Three-left figure demonstrates the contract discontinuity for different set of zero at the same time moment. It's important to note that bubble growth in case of Rihvaya-Meshkov-White instability, three-left pictures, slows down when it starts to interact with the Nagy-Boring entropy vortex cells. The most right figure is the Rihvaya-Meshkov instability calculation with the same value of instability factor. It's clear that mechanism of Rihvaya-Meshkov instability and Rihvaya-Meshkov-White instability development is different. Finally, we present instability development for different cases and the dependencies for the mixing zone width. Comparing cases, cases one and two, which differ only by the form of initial inhomogenities, tessellite-like and strip-like. We note forward in fact, at the early stage of instability development, mixing zone width is the same for the both cases, at the early stage, case one and two. At the later stage, the difference is due to interaction of the bubble with the Nagy-Boring entropy vortex cell in the case two, this bubble interacts with Nagy-Boring entropy vortex cell. This interaction slows down the bubble growth in case two, but the spike growth is equal for both cases. Also, we see that mixing zone width strongly depends on the value of set of zero, see this figure. It's important to note that set of zero defines not only the size of entropy vortex cells, but also initial velocity of spike and bubble. The velocity is greater as set of zero is greater. And finally, conclusion, we describe point of discontinuity stability in the presence of density inhomogenities. For this, we use nonlinear analysis, up to sorts, or the corrections to hydrodynamic quantities. Threatical results of our analysis for bubble growth is in a good agreement with numerical calculations. The question about spike growth is open. Quantity characteristics of instability development strongly depends on angle of initial inhomogenities. Thank you for your attention. Why vector and normal to shock front? Yes. Yes. Yes. Yes. Already. In radians. Yes. Normal. Close to normal. Yes. Yes. No. No. No. No. No. No. Normal. Close to normal. Yes. Yes. Yes. No. No. No. No. One close to normal and its normal and vector amplitude shock front set of zero this. Yes, yes, yes, yes. This angle is normal. Set a zero, practical. 1.4, this angle, 90. 90. Shock front, wave vector, set a zero. Set a zero, practically normal. Set a zero, yes, yes. This tessellite type with initial homogenities is sum of two core signals. It's a tessellite type structure, no strip line. It's a tessellite type. Initial structure.