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Solution. The PDE may be rewritten as ∇u·(a,b) = 0. This means that all solutions are constant along curves with directionDefinitions of different type of PDE (linear, quasilinear, semilinear, nonlinear). • Existence and uniqueness of solutions. • Solving PDEs analytically is To predict weather one need "only" solve a very large systems of coupled PDE equations for momentum, pressure, moisture, heat, etc. Page 5. 5. Conservación de 1.2 Solving and Interpreting a Partial Differential Equation 3. 2 Fourier Series (a) The general solution in Exercise 5 is u(x, t) = f(x + t).