Article Contents
Article Contents

# Heat equation with a nonlinear boundary condition and uniformly local $L^r$ spaces

• We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local $L^r$ spaces. Furthermore, we study the sharp lower estimates of the blow-up time of the solutions with the initial data $\lambda\psi$ as $\lambda\to 0$ or $\lambda\to\infty$ and the lower blow-up estimates of the solutions.
Mathematics Subject Classification: Primary: 35B44, 35K55, 35K60.

 Citation:

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