Chapter 1 First order Partial Differential Equations Sec
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Chapter 1: First order Partial Differential Equations Sec 1. 3: The significance of characteristics Given PDE Cauchy Given ODE Problem IVP Initial Value Problem cauchy data curve Initial data
Chapter 1: First order Partial Differential Equations Sec 1. 3: The significance of characteristics Given PDE Cauchy Problem Consider: Find a solution satisfying on the ellipse cauchy data curve
Chapter 1: First order Partial Differential Equations Sec 1. 3: The significance of characteristics Summary: (Cauchy Problem) Examples suggest that we can expect a unique solution of a cauchy problem if the curve is not characteristic and no solution or infinitely solutions if the curve is characteristic. Unique No solution Inf. solutions
Chapter 1: First order Partial Differential Equations Sec 1. 3: The significance of characteristics This PDE has general sol: Find a solution satisfying on the line WHY? Charac:
Chapter 1: First order Partial Differential Equations Sec 1. 3: The significance of characteristics This PDE has general sol: Find a solution satisfying on the parabola WHY? Charac:
Chapter 1: First order Partial Differential Equations Sec 1. 3: The significance of characteristics Summary: (Cauchy Problem) Examples suggest that we can expect a unique solution of a cauchy problem if the curve is not characteristic and no solution or infinitely solutions if the curve is characteristic. Unique No solution Inf. solutions Characterestics have some significance in the context of existence and uniqueness of solutions
Chapter 1: First order Partial Differential Equations Sec 1. 3: The significance of characteristics Find a solution satisfying on the line This PDE has general sol: Characteristic curves:
