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Growth order and blow up points for the parabolic Burgers' equation under dynamical boundary conditions

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  • We investigate the blow up points of the one--dimensional parabolic Burgers' equation $$\partial_t u=\partial_x^2 u-u\partial_xu+u^p $$ under a dissipative dynamical boundary condition $\sigma \partial_t u+\partial_\nu u=0$ for one bump initial data. A numerical example of a solution pertaining exactly two bumps stemming from its initial data is presented. Moreover, we discuss the growth order of the $L^\infty$--norm of the solutions when approaching the blow up time.
    Mathematics Subject Classification: 35K55, 35K20, 35B44.


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