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A priori estimates of global solutions of superlinear parabolic problems without variational structure

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  • We consider various classes of superlinear parabolic problems, including reaction-diffusion systems and scalar reaction-diffusion equations with convective or dissipative gradient terms. For these problems we prove uniform a priori estimates for all nonnegative global solutions. The existence of an energy functional for these problems is not known, so that traditional methods for a priori estimates do not apply. We use a different approach based on scaling and Fujita-type theorems. In the case of reaction-diffusion systems, we also obtain some universal bounds, i.e. a priori estimates independent of the initial data.
    Mathematics Subject Classification: Primary: 35B45, 35K45, 35K55.


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