Second‐Order Parabolic Differential Equations

By D. Duffy. 2013

1,020 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/80f70d8e8ee26574ed0274d648073db251ad85a5

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Linear and Quasi-Linear Evolution Equations in Hilbert Spaces (2012, background): “, to Ladyzenshkaya, Solonnikov and Ural’tseva [86], Amann [6], Pao [131], Lunardi [107], Lieberman [96], and Krylov [83, 84], where these equations are mostly studied in the Hölder spaces Cm+α/2,2m+α(Q).”
Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012, neutral): “15 of Liebermann [15] that there exist vα,α′ , vα,α′ ∈ C1,2(Qα) ∩ C(Q α ) solutions of the equations: ( Eα,α′ ) : −∂tv − gα′(.”
Periodic pyramidal traveling fronts of bistable reaction-diffusion equations with time-periodic nonlinearity (2012, background): “On the other hand, in B(0; r2) the interior estimates (see [32]) yield”
A NONLINEAR PARABOLIC-HYPERBOLIC SYSTEM FOR CONTACT INHIBITION OF CELL-GROWTH (2012, background): “By Agmon-DouglisNirenberg type interior Lp estimates ([16], p.”
Dynamics of strongly competing systems with many species (2012, neutral): “9 (combining it with a standard a priori estimate of the heat equation, see page 17 in [25]), vl is Lipschitz with a Lipschitz constant less than 3, so if vl(x, t) ≥ 2hl, there is a cylinder of size ∼ hl such that on this”
Regularity and Asymptotic Behavior of Nonlinear Stefan Problems (2014, neutral): “27 in [19]), we can find a constant C such that, for any t ≥ T + 3,”
Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems (2014, neutral): “[26] G.M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, River Edge, NJ, 1998.”
An Introduction to Fully Nonlinear Parabolic Equations (2013, background): “Very nice books such as [20, 17, 7, 21] are attempt to gather and order the most significant advances in this wide field.”
Degenerate parabolic stochastic partial differential equations (2013, background): “The literature devoted to the existence of a classical solution to deterministic parabolic problems is quite extensive, let us mention for instance the works of Friedman [25], Grunau, von Wahl [28], Ladyzhenskaya, Solonnikov, Ural’ceva [51], Lieberman [53], von Wahl [77], Yagi [79] and the reference”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, methodology): “We refer to the books [135, 179] for the elliptic theory, and to [125, 178, 183] for the parabolic theory.”