Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source
Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source
This paper is devoted to understand the blow-up properties of reaction-diffusion equations which combine a localized reaction term with nonlinear diffusion. In particular, we study the critical exponent of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-Laplacian equation with a localized reaction. We obtain the Fujita exponent<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>of the equation.