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Nonlinear parabolic equations with critical growth and superlinear reaction terms

A. El Hachimi, J. Igbiga


This paper is devoted to deal with existence results concerning non linear parabolic equations with general quadratic gradient terms and with superlinear reaction terms which depend on the solution. We point out that no boundedness is assumed on the data of the problem. We give an existence result of distributional solution via test-function method. The method of sub-supersolution do not apply here. Our method relies on a priori estimates and compactness arguments. We also give some examples and remarks which show the optimality of the obtained results.

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