A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, 2006 To book contents

T8. Linear Equations and Problems of Mathematical Physics

• T8.1. Parabolic Equations
  • T8.1.1. Heat Equation w_t = aw_xx
  • T8.1.2. Nonhomogeneous Heat Equation w_t = aw_xx + Φ(x, t)
  • T8.1.3. Equation of the Form w_t = aw_xx + bw_x + cw + Φ(x, t)
  • T8.1.4. Heat Equation with Axial Symmetry w_t = a(w_rr + r⁻¹w_r)
  • T8.1.5. Equation of the Form w_t = a(w_rr + r⁻¹w_r) + Φ(r, t)
  • T8.1.6. Heat Equation with Central Symmetry w_t = a(w_rr + 2r⁻¹w_r)
  • T8.1.7. Equation of the Form w_t = a(w_rr + 2r⁻¹w_r) + Φ(r, t)
  • T8.1.8. Equation of the Form w_t = aw_xx + (1 − 2β)x⁻¹w_x
  • T8.1.9. Equations of the Diffusion (Thermal) Boundary Layer
  • T8.1.10. Schrodinger Equation iw_t = −kw_xx + U(x)w
• T8.2. Hyperbolic Equations
  • T8.2.1. Wave Equation w_tt = a²w_xx
  • T8.2.2. Equation of the Form w_tt = a²w_xx + Φ(x, t)
  • T8.2.3. Klein--Gordon Equation w_tt = a²w_xx − bw
  • T8.2.4. Equation of the Form w_tt = a²w_xx − bw + Φ(x, t)
  • T8.2.5. Equation of the Form w_tt = a²(w_rr + r⁻¹w_r) + Φ(r, t)
  • T8.2.6. Equation of the Form w_tt = a²(w_rr + 2r⁻¹w_r) + Φ(r, t)
  • T8.2.7. Equations of the Form w_tt + kw_t = a²w_xx + bw
• T8.3. Elliptic Equations
  • T8.3.1. Laplace Equation Δw = 0
  • T8.3.2. Poisson Equation Δw + Φ(x) = 0
  • T8.3.3. Helmholtz Equation Δw + λw = −Φ(x)
• T8.4. Fourth-Order Linear Equations
  • T8.4.1. Equation of the Form w_tt + a²w_xxxx = 0
  • T8.4.2. Equation of the Form w_tt + a²w_xxxx = Φ(x, t)
  • T8.4.3. Biharmonic Equation ΔΔw = 0
  • T8.4.4. Nonhomogeneous Biharmonic Equation ΔΔw = Φ(x, y)
• References for Chapter T8

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