1. Dimensional Analysis and Similarity.- 1. Dimensions.- 2. Dimensional Analysis.- 3. Similarity.- 2. The Application of Dimensional Analysis to the Construction of Exact Special Solutions to Problems of Mathematical Physics. Self-Similar Solutions.- 1. Strong Thermal Waves.- 2. Strong Blast Waves.- 3. Self-Similarity. Intermediate Asymptotics.- 3. Modified Problem of an Instantaneous Heat Source: Self-Similar Solution of the Second Kind.- 1. Modified Problem of an Instantaneous Heat Source.- 2. Derivation of the Basic Equation.- 3. Direct Application of Dimensional Analysis to the Modified Problem of an Instantaneous Heat Source.- 4. Resolution of the Paradox. Self-Similar Intermediate Asymptotics. Nonlinear Eigenvalue Problem.- 5. Numerical Calculations.- 4. The Problem of a Strong Explosion with Energy Loss or Deposition at the Front of the Shock Wave and the Problem of an Impulsive Load: Self-Similar Solutions of the Second Kind.- 1. Statement of the Modified Problem of a Strong Explosion.- 2. Direct Application of Dimensional Analysis to the Modified Problem of a Strong Point Explosion.- 3. Resolution of the Paradox. Intermediate Asymptotics.- 4. Qualitative Investigation of a Nonlinear Eigenvalue Problem.- 5. Numerical Calculations.- 6. The Problem of an Impulsive Load.- 7. Numerical Calculations. Self-Similar Asymptotics.- 8. Self-Similar Limiting Solution.- 9. Laws of Conservation of Energy and Momentum in the Problem of an Impulsive Load.- 5. Classification of Self-Similar Solutions.- 1. Complete and Incomplete Self-Similarity.- 2. Self-Similar Solutions of the First and Second Kinds.- 6. Self-Similar Solutions and Progressive Waves.- 1. Solutions of Progressive-Wave Type.- 2. Burgers Shock Wave-Steady Progressive Wave of the First Kind.- 3. Flame-Steady Progressive Wave of the Second Kind.- 4. Nonlinear Eigenvalue Problem.- 7. Self-Similarity and Transformation Groups.- 1. Dimensional Analysis and Transformation Groups.- 2. The Boundary Layer on a Flat Plate.- 3. Limiting Self-Similar Solutions.- 4. Rotation of Fluid in a Cylindrical Container.- 8. The Spectrum of Exponents in Self-Similar Variables.- 9. Stability of Self-Similar Solutions.- 10. Self-Similar Intermediate Asymptotics of Some Linear Problems in the Theory of Elasticity and the Hydrodynamics of Ideal Fluids.- 1. The Problem of the Equilibrium of an Elastic Wedge under the Action of a Concentrated Couple Applied at Its Tip.- 2. The Sternberg-Koiter Paradox. Intermediate Asymptotics of the Non-Self-Similar Problem.- 3. The Use of Self-Similar Solutions for Estimating the Stiffness of a Wedge.- 4. The Flow of Ideal Incompressible Fluid in a Corner—Self-Similar Solution of the Second Kind.- 11. Self-Similarities of the First and Second Kind in the Theory of Turbulence. Homogeneous Isotropic Turbulence.- 1. The Problem of Turbulence.- 2. Homogeneous Isotropic Turbulence.- 3. The Decay of Homogeneous Isotropic Turbulence for Negligibly Small Third Moments.- 4. The Decay of Homogeneous Isotropic Turbulence for Finite Third Moments.- 5. Locally Isotropie Turbulence.- 12. Self-Similarities of the First and Second Kind in the Theory of Turbulence. Shear Flow.- 1. The Wall Region of a Turbulent Shear Flow.- 2. Similarity Laws for the Atmospheric Surface Layer.- 3. Similarity Laws for Flow in a Turbulent Wall Region with Adverse Pressure Gradient.- 4. Unsteady Phenomena in the Viscous Layer of a Turbulent Shear Flow.- 5. The Regime of Limiting Saturation of a Turbulent Shear Flow Loaded with Sediment.- Epilogue.- References.
