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Fundamental solutions for degenerate parabolic equations [PDF]
Acta Mathematica, 1974 This chapter explains the construction of a candidate for a fundamental solution and the existence, smoothness, and certain bounds for a fundamental solution Γ. The underlying assumptions were that ( a ij , ( x )) is uniformly positive definite and a ij , b i are bounded and uniformly Holder continuous. The chapter presents a proof of how if a ij ,
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Asymptotic expansions for degenerate parabolic equations
Comptes Rendus. Mathématique, 2014 We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short-time ...
PASCUCCI, ANDREA +2 more
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A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations
Abstract and Applied Analysis, 2011 We consider a cooperating two-species Lotka-Volterra model of degenerate parabolic equations. We are interested in the coexistence of the species in a bounded domain.
Jiebao Sun, Dazhi Zhang, Boying Wu
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Asymptotic behavior for parabolic equations with interior degeneracy
Examples and Counterexamples, 2022 The long time behavior of a class of degenerate parabolic equations in a bounded domain will be considered in the sense that the nonnegative diffusion coefficient a(x)is allowed to vanish in a set of positive measure in the interior of the domain.
María Astudillo +3 more
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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
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Mixed problems for degenerate abstract parabolic equations and applications [PDF]
, 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 ...
Sahmurova, Aida, Shakhmurov, Veli
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Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation
, 2015 We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to recent trends in diffusion theory: considering anomalous diffusion with ...
Carrillo, Jose Antonio +1 more
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On the Cauchy Problem for a Degenerate Parabolic Equation
Zeitschrift für Analysis und ihre Anwendungen, 2001 Existence and uniqueness of global positive solutions to the degenerate parabolic problem u_t = f(u)\Delta u \ \ \mathrm {in} \ \ \mathbb R^n \times (0, \infty) u|_{t=0} = u–0 with
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On a Class of Degenerate Abstract Parabolic Problems and Applications to Some Eddy Current Models
, 2020 We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation may admit a type change ranging from parabolic to elliptic type problems.
Pauly, Dirk +3 more
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Gradient estimates for degenerate quasi-linear parabolic equations
, 2010 For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients form bounded with respect to the Laplacian we obtain $L^q$-estimates for the gradients of solutions, and for the
Liskevich, Vitali +2 more
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