Results 231 to 240 of about 2,128,627 (261)
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Global Attractor of One Nonlinear Parabolic Equation
Ukrainian Mathematical Journal, 2003Let \(\Omega \) be a domain in \(\mathbb R^n\) with smooth boundary \(\partial \Omega \), \(\Omega_T:=[0,T]\times \Omega \). The authors consider the Cauchy-Dirichlet problem \[ \begin{gathered} u_t=a\Delta u-f(u)+\lambda u+\langle {\mathbf b}({\mathbf x}),\nabla u \rangle -g({\mathbf x});\tag{1} \\ u\big|_{\partial \Omega}=0,\quad u\big|_{t=0}=u_0 ...
Kapustyan, O. V., Shkundin, D. V.
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Asymptotic Behavior of the Nonlinear Parabolic Equations
Journal of Partial Differential Equations, 2004This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces R^n. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data u_0 ∈ L² ∩ L^r for 1 ≤ r ≤ 2, then the solutions decay in L² norm at t^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2})}.
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On a Class of Fully Nonlinear Parabolic Equations
Communications in Partial Differential Equations, 1991We consider a class of intial boudnary value problems for parabolic equaitons of the form u$sub:t$esub:=f(t,x,u,Du,au) in a bounded domain Ω where A is an elliptic operator with continous coefficients. Scuh problems can be modeled by nonlinear evolation equaitons in Banach spaces, and we use abstract parabolic equairtions technique to show existence ...
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On some parabolic equations with mon ditferentiable nonlinearities
Communications in Partial Differential Equations, 1982(1982). On some parabolic equations with mon ditferentiable nonlinearities. Communications in Partial Differential Equations: Vol. 7, No. 12, pp. 1439-1452.
DE MOTTONI P +2 more
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Nonlinear parabolic equations for measures
St. Petersburg Mathematical Journal, 2012Summary: A new existence result is established for weak parabolic equations for probability measures. Sufficient conditions are given for the existence of local and global-in-time probability solutions of the Cauchy problem for such equations. Some conditions under which global-in-time solutions do not exist are indicated.
Manita, O. A., Shaposhnikov, S. V.
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Some degenerate nonlinear parabolic equations
九州大学教養部数学雑誌, 1984The author proves existence, uniqueness and asymptotic behaviour of solutions of the initial value problem for the generalized porous medium equation on a bounded domain in \({\mathbb{R}}^ n\). In various cases, decay notes, positivity and uniqueness are given which extend known results in various directions.
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Parabolic equations with operator nonlinearity
Asian-European Journal of MathematicsIn this paper, we consider partial differential equations (PDE) of parabolic type with functional nonlinearity in the reaction summand. Our goal is to give the answer of the question if there exist a set of smooth functions satisfying the inequality [Formula: see text], where [Formula: see text] is a parabolic operator in the parabolic PDE with a ...
Saba Iftikhar +4 more
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Mathematical Tables and Other Aids to Computation, 1948
Bruce L. Hicks, H. G. Landau
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Bruce L. Hicks, H. G. Landau
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On boundary value problems for nonlinear parabolic equations
1957zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Nonlinear Schrödinger Equation Including the Parabolic Law and Its Dark Solitons
Optik, 2023Evren Hincal +2 more
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