A method of energy estimates in L<SUP>∞</SUP> and its application to porous medium equations

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  • ÔTANI Mitsuharu
    Department of Applied Physics School of Science and Engineering Waseda University
  • SUGIYAMA Yoshie
    Department of Mathematics and Computer Science Department of Mathematics School of Science and Engineering Waseda University

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  • A method of energy estimates in L∞ and its application to porous medium equations--Dedicated to Professor Kyuya MASUDA on the occasion of his 60-th birthday
  • method of energy estimates in L and its application to porous medium equations Dedicated to Professor Kyuya MASUDA on the occasion of his 60 th birthday
  • A method of energy estimates in L∞ and its application to porous medium equations
  • Dedicated to Professor Kyuûya MASUDA on the occasion of his 60-th birthday

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The existence of time local C∞-solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the“ L∞-energy method”developed in our previous paper [{16}] and a new method based on the theory of evolution equations in the L2-framework which enables us to handle with perturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.

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