Results 21 to 30 of about 3,896 (168)

Degenerate parabolic equations appearing in atmospheric dispersion of pollutants

Electronic Journal of Qualitative Theory of Differential Equations, 2016
Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equation and boundary conditions are degenerated on all boundary and contain some parameters.
Veli Shakhmurov, Aida Sahmurova
doaj   +1 more source

Nonlinear Parabolic Equations with Measure Data

Journal of Functional Analysis, 1997
Consider the parabolic problem \[ u_t -\mathop{div} a(x,t,u,Du) = \mu \quad\text{in } Q,\qquad u = 0 \quad \text{on } \mathcal PQ, \] where \(a(x,t,z,\xi)\) behaves like \(|\xi|^{p-2}\xi\), \(Q\) is a space-time cylinder with parabolic boundary \(\mathcal PQ\), and \(\mu\) is a measure on \(Q\).
BOCCARDO, Lucio, DALL'AGLIO, Andrea, Thierry Gallouet, ORSINA, Luigi   +3 more
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Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations

Advances in Nonlinear Analysis, 2020
This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth
Grunau Hans-Christoph, Miyake Nobuhito, Okabe Shinya   +2 more
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Bounded Solutions to Nonlinear Parabolic Equations [PDF]

ISRN Mathematical Analysis, 2011
We deal with existence results for nonlinear parabolic equations with general quadratic gradient terms and with absorption term which depend on the solution. We note that no boundedness is assumed on the data of the problem. We prove an existence result of distributional solution via test-function method.
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Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

Mathematics
The optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic ...
Yang Na, Tianjiao Men, Runmei Du, Yingjie Zhu   +3 more
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Nonlinear Parabolic Equations with Regularized Derivatives

Journal of Mathematical Analysis and Applications, 1999
Nonlinear systems of differential equations \[ \partial_tu+\partial_xf(u)+g(u)=\Delta u\tag{1} \] are considered on \(\mathbb R_+^{n+1}\) \((t>0)\), where \(u=(u_1,\dots,u_m)^T\), \(f(u)=(f_1(u),\dots,f_n(u))^T\), \(\partial_xf(u)=\sum_{i=1}^n\partial_{x_i}f_i(u)\).
Wang, Y.G., Oberguggenberger, M.
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Carleman inequality for a class of super strong degenerate parabolic operators and applications

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed
Bruno Sérgio Araújo, Reginaldo Demarque, Luiz Viana   +2 more
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A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem

Journal of Inequalities and Applications, 2018
In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete
Lin Li, Zuliang Lu, Wei Zhang, Fei Huang, Yin Yang   +4 more
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To the uniqueness problem for nonlinear parabolic equations

Discrete and Continuous Dynamical Systems, 2004
Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
Skrypnik, Igor V., Gajewski, Herbert
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A nonlinear parabolic equation modelling surfactant diffusion [PDF]

European Journal of Applied Mathematics, 2000
An initial-boundary value problem for nonlinear parabolic equations modelling surfactant diffusions is investigated. The boundary conditions are of nonlinear adsorptive types, and the initial value has a single point jump. We study the well-posedness of the problem, the convergence of a numerical scheme, and the regularity as well as quantitative ...
Chen, Xinfu, Huang, Chaocheng, Zhao, Jennifer   +2 more
openaire   +4 more sources