Results 41 to 50 of about 1,312 (223)
Global Sobolev Solutions of Quasilinear Parabolic Equations
Differential and Integral Equations, 1998 Global existence, uniqueness and a priori estimates of solutions to the initial and homogeneous Dirichlet boundary value problem for the equation \[ u_t - \sum _{i,j=1}^{n} a_{i,j}(\nabla u) \partial _i \partial _j u = f(x,t)\quad\text{on} \Omega \times (0,T) \] is proved in Sobolev spaces \(X_{s+2}(T)\) for sufficiently large \(s.\) Here \[ X_m(T) = \{
McLeod, Kevin, Milani, Albert
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Convergence of quasilinear parabolic equations to semilinear equations
Discrete and Continuous Dynamical Systems - B, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bezerra, Flank D. M. +2 more
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On the principle of linearized stability for quasilinear evolution equations in time‐weighted spaces
Mathematische Nachrichten, Volume 298, Issue 12, Page 3939-3959, December 2025.Abstract Quasilinear (and semilinear) parabolic problems of the form v′=A(v)v+f(v)$v^{\prime }=A(v)v+f(v)$ with strict inclusion dom(f)⊊dom(A)$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function v↦f(v)$v\mapsto f(v)$ and the quasilinear part v↦A(v)$v\mapsto A(v)$ are considered in the framework of time‐weighted function spaces ...
Bogdan‐Vasile Matioc +2 more
wiley +1 more source
Mathematical Modelling and Analysis, 2021 The main aim of this paper is to present a hybrid scheme of both meshless Galerkin and reproducing kernel Hilbert space methods. The Galerkin meshless method is a powerful tool for solving a large class of multi-dimension problems.
Mehdi Mesrizadeh, Kamal Shanazari
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On an Inverse Problem for Quasilinear Parabolic Equations
Tokyo Journal of Mathematics, 1998 Under specific conditions the problem of identifying the parameter function \(a(x,u)\) in the initial-boundary value problem \[ u_t- a(x,u) u_{xx}= 0,\quad ...
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
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A Model of Porous Catalyst Accounting for Incipiently Non-isothermal Effects*
, 1999 An approximate model accounting for incipiently non-isothermal effects is derived from a well-known model of porous catalyst for appropriate, realistic limiting values of the parameters.
Vega de Prada, José Manuel +3 more
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Muskat–Leverett Two‐Phase Flow in Thin Cylindric Porous Media: Asymptotic Approach
Studies in Applied Mathematics, Volume 155, Issue 5, November 2025.ABSTRACT A reduced‐dimensional asymptotic modeling approach is presented for the analysis of two‐phase flow in a thin cylinder with an aperture of order O(ε)$\mathcal {O}(\varepsilon)$, where ε$\varepsilon$ is a small positive parameter. We consider a nonlinear Muskat–Leverett two‐phase flow model expressed in terms of a fractional flow formulation and
Taras Mel'nyk, Christian Rohde
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Steady-state solutions of a mass-conserving bistable equation with a saturating flux
, 2012 We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein–Steinberg equation, suitable for description of order parameter conserving solid–solid phase transitions in the case
Grinfeld, Michael +3 more
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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 ...
ter Elst, A. F. M. +6 more
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