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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2019 • Question 8

Question

Math 6410 • ODE Fall 2019 • Question 8

Show that the heat/diffusion equation with the wrong sign \(u_t=-u_{xx}\) is extremely unstable (and so, the Cauchy problem for this equation is ill posed in the sense of Hadamard).

Raw LaTeX

Show that the heat/diffusion equation with the wrong sign \(u_t=-u_{xx}\) is extremely
unstable (and so, the Cauchy problem for this equation is ill posed in the sense of
Hadamard).

Topic Tags

Heat Equation and Parabolic Equations Reaction-Diffusion-Advection Equations