Artículos de revistas
Evolution Pde With Elliptic Dissipative Terms: Critical Index For Singular Initial Data, Self-similar Solutions And Analytic Regularity [edp D'évolution Avec Dissipation Elliptique : L'indice Critique Pour Des Données Initiales Singulières, Solutions Auto-similaires Et Régularité Analytique]
Registro en:
Comptes Rendus De L'academie Des Sciences - Series I: Mathematics. , v. 327, n. 1, p. 41 - 46, 1998.
7644442
2-s2.0-0032110796
Autor
Biagioni H.A.
Gramchev T.
Institución
Resumen
We investigate the influence of the elliptic dissipative terms of evolution equations in ℝn and double-struck T signn on the critical Lp, 1 ≤ p ≤ ∞, index of the singularity of the initial data, the analytic regularity for positive time and the existence of self-similar solutions. © Académie des Sciences/Elsevier, Paris. 327 1 41 46 Bekhiranov, D., The initial value problem for the generalized Burgers' equation (1996) Differ. Integ. Eq., 9, pp. 1253-1265 Biagioni, H.A., Cadeddu, L., Gramchev, T., Parabolic equations with conservative nonlinear term and singular initial data, Proc. 2nd World Congress of Nonlinear Analysts (1997) Nonlin. Anal. TMA, 30, pp. 2489-2496. , Athens, Greece, July 10-17, 1996 Brézis, H., Friedman, H., Nonlinear parabolic equations involving measures as initial conditions (1983) J. Math. Pures Appl., 62, pp. 73-97 Brézis, H., Cazenave, T., Nonlinear heat equation with singular initial data (1996) J. Anal. Math., 68, pp. 276-304 Cannone, M., Planchon, F., Self-similar solutions for Navier-Stokes equations in ℝ3, Commun (1996) Partial Differ, Eq., 21, pp. 179-193 Chemin, J.-Y., Fluides parfaits incompressibles (1995) Astérisque, 230, pp. 1-177 Dix, D., Nonuniqueness and uniqueness in thé initial value problem for Burgers' equation (1996) SIAM J. Math. Anal., 27, pp. 709-724 Ferrari, A., Titi, E., Gevrey regularity for nonlinear analytic parabolic equations (1998) Commun. Partial Differ. Eq., 23, pp. 1-16 Foias, C., Temam, R., Gevrey class regularity for the solutions of the Navier-Stokes equations (1989) J. Funct. Anal., 87, pp. 359-369 Kozono, H., Yamazaki, M., Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data (1994) Commun. Partial Differ. Eq., 19, pp. 959-1014 Levermore, D., Oliver, M., Distribution-valued initial data for the complex Ginzburg-Landau equation (1997) Commun. Partial Differ. Eq., 22, pp. 39-49 Planchon, F., Convérgence des solutions des équations de Navier-Stokes vers des solutions auto-similaires (1996) Séminaire X-EDP, 95-96 Ribaud, F., (1996) Analyse de Littlewood-Paley Pour la Résolution d'Équations Paraboliques Semi-linéaires, , Thèse de Docteur en Sciences, Orsay Bollerman, P., Doelman, A., Van Harten, A., Titi, E., Analyticity for essentially bounded solutions to strongly parabolic semilinear systems (1996) SIAM J. Math. Anal., 27, pp. 424-448