Results 11 to 20 of about 12,988 (199)

The applications of Sobolev inequalities in proving the existence of solution of the quasilinear parabolic equation

Boundary Value Problems, 2020
The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations.
Yuanfei Li, Lianhong Guo, Peng Zeng
doaj   +1 more source

On maximal parabolic regularity for non-autonomous parabolic operators [PDF]

, 2016
We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time ...
A.F.M. ter Elst, Adams, Agmon, Alt, Amann, Amann, Amann, Amann, Arendt, Arendt, Arendt, Arendt, Auscher, Bergh, Brewster, Cannarsa, Casas, Clément, Dautray, De Simon, Denk, Disser, Disser, Disser, Dong, Dong, Dore, Dore, Dore, Egert, Egert, Elschner, Elschner, Evans, Fackler, Fackler, Gallarati, Grisvard, Grisvard, Gröger, Haller-Dintelmann, Haller-Dintelmann, Haller-Dintelmann, Haller-Dintelmann, Haller-Dintelmann, Hieber, Hömberg, Jerison, Joachim Rehberg, Jonsson, Karoline Disser, Krumbiegel, Kunisch, Köhne, Lamberton, Lang, Lions, Maz'ja, Morrey, Prüss, Prüss, Prüss, Schnaubelt, Sneiberg, Tamm, ter Elst, ter Elst, ter Elst, Triebel, Vignati, Weis, Zanger   +71 more
core   +3 more sources

Depleting the signal: Analysis of chemotaxis‐consumption models—A survey

Studies in Applied Mathematics, Volume 151, Issue 4, Page 1197-1229, November 2023., 2023
Abstract We give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis‐consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures.
Johannes Lankeit, Michael Winkler
wiley   +1 more source

Flow relaxation method in solving quasilinear parabolic equations [PDF]

Компьютерные исследования и моделирование, 2011
This article proposes a numeric method of solution of quasilinear parabolic equations, based on the flux approximation, describes the implementation of the method on a rectangular grid and presents numerical results.
Alexey I. Lobanov, V. A. Usenko
doaj   +1 more source

Constrained Evolution for a Quasilinear Parabolic Equation [PDF]

Journal of Optimization Theory and Applications, 2016
In the present contribution, a feedback control law is studied for a quasilinear parabolic equation. First, we prove the well-posedness and some regularity results for the Cauchy--Neumann problem for this equation, modified by adding an extra term which is a multiple of the subdifferential of the distance function from a closed convex set K of L<sup&
P Colli, G Gilardi, J Sprekels
openaire   +6 more sources

On quasilinear parabolic evolution equations in weighted Lp-spaces II [PDF]

, 2013
Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity.
D. Bothe, J. Prüss, Jan Prüss, Jeremy LeCrone, M. Meyries, M. Meyries, Mathias Wilke   +6 more
core   +3 more sources

Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data

Journal of Function Spaces, 2018
We study the Cauchy problem of the quasilinear evolution equations in Lμp-spaces. Based on the theories of maximal Lp-regularity of sectorial operators, interpolation spaces, and time-weighted Lp-spaces, we establish the local posedness for a class of ...
Qinghua Zhang
doaj   +1 more source

Nonlinear second order evolution equations with state-dependent delays

Electronic Journal of Qualitative Theory of Differential Equations, 2012
We consider second order quasilinear parabolic equations where also the main part contains functional dependence and state-dependent delay on the unknown function. Existence and some qualitative properties of the solutions are shown.
László Simon
doaj   +1 more source

Critical Exponents of Quasilinear Parabolic Equations

Journal of Mathematical Analysis and Applications, 2002
The critical exponent for the global existence of positive solutions of the equation \[ u_t = \text{div}(|\nabla u|^{m-1}\nabla u)+t^s|x|^\sigma u^p \] in \(\mathbb R^n\) is found for \(s\geq 0\), \((n-1)/(n+1)n(1-m)-1-m-2s.\)
Qi, YW, Wang, MX
openaire   +2 more sources

Quasilinear evolution equations and parabolic systems [PDF]

Transactions of the American Mathematical Society, 1986
It is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values, provided the boundary conditions are “time-independent”. Moreover it is shown that, in the autonomous case, these equations generate local semiflows on appropriate Sobolev spaces. Our results apply, in particular, to
openaire   +1 more source