| Abstract: |
| We consider the existence and nonexistence of global solutions to the initial-boundary value problem of nonlinear heat equations on a bounded domain. For nonlinear heat equations in the whole space, it is well known that there exists the critical Fujita exponent which gives the threshold that divides the existence and nonexistence of positive global solutions. On the other hand, as for the same equation in bounded domains, there is no such critical exponent. In this talk, however, we show that a similar threshold phenomenon can occur in bounded domains, which is controlled according to boundary conditions but not to the exponent of a nonlinear term. |
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