Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in L
      p

Albert N. Sandjo; Célestin Wafo Soh

Displaying similar documents to “ Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in L p ”

Time and space Sobolev regularity of solutions to homogeneous parabolic equations

Gabriella Di Blasio (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We give necessary and sufficient conditions on the initial data such that the solutions of parabolic equations have a prescribed Sobolev regularity in time and space.

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Mikhail Borsuk (2002)

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We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.

Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_{p}$ -space

Marián Slodička (1989)

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The Rothe-Galerkin method is used for discretization. The rate of convergence in $C (I, L_{p} (G))$ for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established.

Local Existence and Regularity for a Class of Degenerate Parabolic Equations.

Sigurd Angenent (1988)

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Transition from decay to blow-up in a parabolic system.

Quittner, Pavol (1998)

Archivum Mathematicum

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Characterization of the interior regularity for parabolic systems with discontinuous coefficients

Dian K. Palagachev, Lubomira G. Softova (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We deal in this Note with linear parabolic (in sense of Petrovskij) systems of order $2 b$ with discontinuous principal coefficients belonging to $V M O ⋂ L^{\infty}$ . By means of a priori estimates in Sobolev-Morrey spaces we give a precise characterization of the Morrey, BMO and Hölder regularity of the solutions and their derivatives up to order $2 b - 1$ .

Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions

Changchun Liu (2013)

Annales Polonici Mathematici

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We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.

On optimal $L^{p}$ regularity in evolution equations

Alessandra Lunardi (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Using interpolation techniques we prove an optimal regularity theorem for the convolution $u (t) = \int_{0}^{t} T (t - s) f (s) d s$ , where $T (t)$ is a strongly continuous semigroup in general Banach space. In the case of abstract parabolic problems – that is, when $T (t)$ is an analytic semigroup – it lets us recover in a unified way previous regularity results. It may be applied also to some non analytic semigroups, such as the realization of the Ornstein-Uhlenbeck semigroup in $L^{p} (R^{n})$ , $1 < p < \infty$ , in which case it yields new optimal regularity results...