We prove under weak assumptions that solutions of doubly nonlinear reaction-diffusion equations
to initial values are instantly regularized to functions (ultracontractivity). Our proof is based on a priori estimates of for a time-dependent exponent . These a priori estimates can be obtained in an elementary way from logarithmic Gagliardo-Nirenberg inequalities by an optimal choice of , and they do not only imply ultracontractivity, but provide further information about the long-time behaviour.
Published April 15, 2009.
Math Subject Classifications: 35K65, 35B35, 46E35, 35B45.
Key Words: p-Laplacian; doubly nonlinear evolution equations; ultracontractive semigroups; logarithmic Gagliardo-Nirenberg inequalities.
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| Jochen Merker |
University of Rostock, D-18051 Rostock, Germany
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