Results 1 to 10 of about 419,776 (294)
Null controllability of degenerate parabolic equation with memory [PDF]
Mathematical Methods in the Applied Sciences, 2020 In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat equation via new
Brahim Allal, G. Fragnelli
semanticscholar +6 more sources
Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem [PDF]
Inverse Problems, 2019 In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function. Combining this Carleman estimate and an approximate argument, we prove the null controllability of the forward stochastic degenerate parabolic ...
Bin Wu, Qun Chen, Zewen Wang
arxiv +3 more sources
Regularity and geometric character of solution of a degenerate parabolic equation
Bulletin of Mathematical Sciences, 2016 This work studies the regularity and the geometric significance of solution of the Cauchy problem for a degenerate parabolic equation $$u_{t}=\Delta {}u^{m}$$ u t = Δ u m . Our main objective is to improve the H $$\ddot{o}$$ o ¨ lder estimate obtained by
Jiaqing Pan
doaj +3 more sources
Riesz potentials and nonlinear parabolic equations [PDF]
, 2013 The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation.
A. Cianchi +31 more
arxiv +4 more sources
Mixed problems for degenerate abstract parabolic equations and applications [PDF]
arXiv, 2017 Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in mixed $L_{p}$ spaces are obtained.
Sahmurova, Aida, Shakhmurov, Veli
arxiv +4 more sources
A degenerate parabolic equation modelling the spread of an epidemic [PDF]
Annali di Matematica Pura ed Applicata, 1986 We consider the Cauchy problem for a degenerate parabolic equation, not in divergence form, representing the diffusive approximation of a model for the spread of an epidemic in a closed population without remotion. We prove existence and uniqueness of the weak solution, defined in a suitable way, and some qualitative properties.
M. Ughi
openalex +4 more sources
Increasing powers in a degenerate parabolic logistic equation [PDF]
Chinese Annals of Mathematics, Series B, 2012 The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \partial_t u-\Delta u=a u-b(x) u^p \text{in} \Omega\times \R^+, u(0)=u_0, u(t)|_{\partial \Omega}=0 $$ as $p\to +\infty$, where $\Omega$ is a ...
Hugo Tavares, Jose Francisco, Rodrigues
core +4 more sources
Degenerate semilinear parabolic equations [PDF]
Differential and Integral Equations, 1992 Andreas Stahel
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Discontinuous “viscosity” solutions of a degenerate parabolic equation [PDF]
Transactions of the American Mathematical Society, 1990 We study a nonlinear degenerate parabolic equation of the second order. Regularizing the equation by adding some artificial viscosity, we construct a generalized solution. We show that this solution is not necessarily continuous at all points.
M. Bertsch +2 more
semanticscholar +5 more sources
Gaussian bounds for degenerate parabolic equations
Journal of Functional Analysis, 2008 AbstractLet A be a real symmetric, degenerate elliptic matrix whose degeneracy is controlled by a weight w in the A2 or QC class. We show that there is a heat kernel Wt(x,y) associated to the parabolic equation wut=divA∇u, and Wt satisfies classic Gaussian bounds:|Wt(x,y)|⩽C1tn/2exp(−C2|x−y|2t).
David Cruz-Uribe, Cristian Rios
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