An improperly posed estimate for the equation |u|^αu_t=u_xx+F(u)(0 <α <1)

Abstract

The noncharacteristic Cauchy problem of heat equations is not well-posed. But the estimation on the continuous dependence of solutions holds under their prescribed bound and the bound of their Cauchy data. In this paper we show that a similar estimation holds also for some degenerate quasilinear parabolic equation.

Keywords:

• Improperly posed problem
• Noncharacteristic Cauchy problem
• Nonlinear parabolic equation
• Fast diffusion
• AMS Subject Classifications: 35K55
• 35K65
• 35R25

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Kazuya Hayasida *

E-mail: [email protected]