Results 41 to 50 of about 953 (219)

Convergence of quasilinear parabolic equations to semilinear equations

Discrete and Continuous Dynamical Systems - B, 2021
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Bezerra, Flank D. M., Simsen, Jacson, Simsen, Mariza Stefanello   +2 more
openaire   +2 more sources

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, Lina Sophie Schmitz, Christoph Walker   +2 more
wiley   +1 more source

Numerical study on the blow-up rate to a quasilinear parabolic equation [PDF]

, 2017
summary:In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation $u_t = u^2(u_{xx}+u)$. We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently ...
Ishiwata, Tetsuya, Ushijima, Takeo, Anada, Koichi   +2 more
core   +1 more source

Quasilinear Degenerate Evolution Systems Modelling Biofilm Growth: Well‐Posedness and Qualitative Properties

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
wiley   +1 more source

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 ...
openaire   +3 more sources

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
doaj   +1 more source

Simulation of Heat Waves in An Nonlinear Anisotropic Space

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010
For the first time analytical solution of the problem with boundary conditions in the non-linear anisotropic space for the quasilinear parabolic heat equation where heat conductivity tensor's components are temperature functions is obtained.
E. L. Kuznetcova, I. A. Selin, V. F. Formalyov   +2 more
doaj   +1 more source

Remarks on global solutions to the initial-boundary value problem for quasilinear degenerate parabolic equations with a nonlinear source term [PDF]

Opuscula Mathematica, 2019
We give an existence theorem of global solution to the initial-boundary value problem for \(u_{t}-\operatorname{div}\{\sigma(|\nabla u|^2)\nabla u\}=f(u)\) under some smallness conditions on the initial data, where \(\sigma (v^2)\) is a positive ...
Mitsuhiro Nakao
doaj   +1 more source

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
wiley   +1 more source

Monotone Finite-Difference Schemes With Second Order Approximation Based on Regularization Approach for the Dirichlet Boundary Problem of the Gamma Equation

IEEE Access, 2020
We investigate the initial boundary value problem for the Gamma equation transformed from the nonlinear Black-Scholes equation for pricing option to a quasilinear parabolic equation of second derivative.
Le Minh Hieu, Truong Thi Hieu Hanh, Dang Ngoc Hoang Thanh   +2 more
doaj   +1 more source