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Partial Differential Equations
Partial Differential Equations
foundations +6 more results +31 more equations +3 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) definition 10.1: Partial differential equation; order 10.1 Partial differen… definition 10.2: Linear, semilinear, quasilinear 10.2 Linear, semiline… definition 10.3: Principal part and principal symbol 10.3 Principal part a… definition 10.4: The second-order operator 10.4 The second-order… definition 10.6: Type of a second-order operator 10.6 Type of a second… definition 10.10: Characteristic surface 10.10 Characteristic s… definition 10.18: Complete integral; envelope 10.18 Complete integra… definition 10.24: Well-posed problem 10.24 Well-posed probl… definition 10.42: Green's function 10.42 Green's function definition 10.50: Retarded and advanced Green's functions 10.50 Retarded and adv… definition 10.66: Harmonic function 10.66 Harmonic function definition 10.79: Parabolic boundary 10.79 Parabolic bounda… definition 10.83: Weak solution 10.83 Weak solution theorem 10.8: The type is a coordinate invariant 10.8 The type is a co… proposition 10.11: What a characteristic surface is 10.11 What a character… corollary 10.12: Characteristics of the three canonical operators 10.12 Characteristics… proposition 10.13: Canonical form in two variables 10.13 Canonical form i… proposition 10.15: Method of characteristics, first order 10.15 Method of charac… proposition 10.16: Cauchy's characteristic strips 10.16 Cauchy's charact… proposition 10.19: An envelope of solutions is a solution 10.19 An envelope of s… theorem 10.22: Cauchy–Kovalevskaya 10.22 Cauchy–Kovalevsk… proposition 10.25: The backward heat problem is ill posed 10.25 The backward hea… lemma 10.28: The separation constant 10.28 The separation c… proposition 10.29: Time separation reduces the canonical equations to
Helmholtz 10.29 Time separation… theorem 10.34: Separable systems for the Helmholtz operator 10.34 Separable system… theorem 10.36: Solution of the heat problem on an interval 10.36 Solution of the… equation 10.1: eq:pde-dalembertian eq. (10.1) equation 10.2: eq:pde-multi-index eq. (10.2) equation 10.6: eq:pde-congruence eq. (10.6) equation 10.8: eq:pde-characteristic-condition eq. (10.8) equation 10.11: eq:pde-two-variable-matrix eq. (10.11) equation 10.12: eq:pde-two-variable-coefficients eq. (10.12) equation 10.15: eq:pde-fully-nonlinear eq. (10.15) equation 10.22: eq:pde-wave-equation eq. (10.22) equation 10.24: eq:pde-poisson-equation eq. (10.24) equation 10.25: eq:pde-helmholtz-equation eq. (10.25) equation 10.26: eq:pde-schrodinger-equation eq. (10.26) equation 10.28: eq:pde-wave-separated eq. (10.28) equation 10.34: eq:pde-spherical-radial eq. (10.34) The chain of Partial Differential Equations: 39 of 79 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.