Results 51 to 60 of about 1,264,456 (207)
Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data [PDF]
In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates for gradients of solutions to the quasilinear parabolic equations: in a bounded domain , under minimal regularity assumptions on the boundary of domain and on nonlinearity A ...
Nguyen, Quoc-Hung
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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
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Resonance and Quasilinear Parabolic Partial Differential Equations
Journal of Differential Equations, 1993 For a certain quasilinear parabolic equation, the authors prove the existence of a weak periodic solution in an adequate Hilbert space under both resonance and nonresonance conditions. The results are obtained by using a Galerkin-type technique.
Lefton, L.E., Shapiro, V.L.
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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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Existence of extremal periodic solutions for quasilinear parabolic equations
Abstract and Applied Analysis, 1997 In this paper we consider a quasilinear parabolic equation in a bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately ...
Siegfried Carl
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On a quasilinear parabolic integrodifferential equation
Differential and Integral Equations, 1995 The author considers the nonlinear Volterra integrodifferential equation \(u_ t - a* \text{div} h(\text{grad} u) = a*g\), where \(x \in \mathbb{R}^ n\), \(t \geq 0\) and where the initial function \(u(0,x) = w(x)\) is given. The kernel \(a\) satisfies \(a \in L^ 1_{\text{loc}} (\mathbb{R}^ +)\) and the parabolic condition \(\text{Re}\widetilde a ...
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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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Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.ABSTRACT We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales ...
M. van den Bosch, H. J. Hupkes
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Existence of a local strong solution to the beam–polymeric fluid interaction system
Mathematische Nachrichten, Volume 298, Issue 7, Page 2327-2379, July 2025.Abstract We construct a unique local strong solution to the finitely extensible nonlinear elastic (FENE) dumbbell model of Warner‐type for an incompressible polymer fluid (described by the Navier–Stokes–Fokker–Planck equations) interacting with a flexible elastic shell.
Dominic Breit, Prince Romeo Mensah
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Quasilinear Differential Constraints for Parabolic Systems of Jordan‐Block Type
Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.ABSTRACT We prove that linear degeneracy is a necessary conditions for systems in Jordan‐block form to admit a compatible quasilinear differential constraint. Such condition is also sufficient for 2×2$2\times 2$ systems and turns out to be equivalent to the Hamiltonian property.
Alessandra Rizzo, Pierandrea Vergallo
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