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P-adaptive Hermite methods for initial value problems∗

Ronald Chen, Thomas Hagstrom (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...

P-adaptive Hermite methods for initial value problems

Ronald Chen, Thomas Hagstrom (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...

P-adaptive Hermite methods for initial value problems∗

Ronald Chen, Thomas Hagstrom (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...

Parabolic differential-functional inequalities in viscosity sense

Krzysztof Topolski (1998)

Annales Polonici Mathematici

We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.

Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

Vagif S. Guliyev, Mehriban N. Omarova (2016)

Open Mathematics

We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space [...] W˙2,1p,φ(Q,ω) W ˙ 2 , 1 p , ϕ Q , ω .

Partial differential operators depending analytically on a parameter

Frank Mantlik (1991)

Annales de l'institut Fourier

Let P ( λ , D ) = ∑ | α | ≤ m a α ( λ ) D α be a differential operator with constant coefficients a α depending analytically on a parameter λ . Assume that the family { P( λ ,D) } is of constant strength. We investigate the equation P ( λ , D ) 𝔣 λ ≡ g λ where 𝔤 λ is a given analytic function of λ with values in some space of distributions and the solution 𝔣 λ is required to depend analytically on λ , too. As a special case we obtain a regular fundamental solution of P( λ ,D) which depends analytically on λ . This result answers a question of L. Hörmander.

Partial exact controllability of a nonlinear system.

A. K. Nandakumaran, R. K. George (1995)

Revista Matemática de la Universidad Complutense de Madrid

In this article, we prove the partial exact controllability of a nonlinear system. We use semigroup formulation together with fixed point approach to study the nonlinear system.

Partial Hölder continuity for quasilinear parabolic systems of higher order with strictly controlled growth

Mario Marino, Antonino Maugeri (1984)

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

Sfruttando i risultati di [1], si prova che le derivate spaziali D α ⁢ u di ordine | α | con | α | < m - 1 delle soluzioni in Q di un sistema parabolico quasilineare di ordine 2 ⁢ m con andamenti strettamente controllati, sono parzialmente hölderiane in Q con esponente di hölderianità decrescente al crescere di | α | .

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