Results 11 to 20 of about 83 (83)
Regularity for the two‐phase singular perturbation problems
Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 433-459, November 2021., 2021 Abstract We prove that an a priori bounded mean oscillation (BMO) gradient estimate for the two‐phase singular perturbation problem implies Lipschitz regularity for the limits. This problem arises in the mathematical theory of combustion, where the reaction diffusion is modeled by the p‐Laplacian. A key tool in our approach is the weak energy identity.
Aram Karakhanyan
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Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 688-746, September 2021., 2021 Abstract This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in particular on gradient flows in the space of probability measures equipped with the distance arising in the ...
Dohyun Kwon, Alpár Richárd Mészáros
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Functional inequalities for the heat flow on time‐dependent metric measure spaces
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 926-955, September 2021., 2021 Abstract We prove that synthetic lower Ricci bounds for metric measure spaces — both in the sense of Bakry–Émery and in the sense of Lott–Sturm–Villani — can be characterized by various functional inequalities including local Poincaré inequalities, local logarithmic Sobolev inequalities, dimension independent Harnack inequality, and logarithmic Harnack
Eva Kopfer, Karl‐Theodor Sturm
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Boundary spike‐layer solutions of the singular Keller–Segel system: existence and stability
Proceedings of the London Mathematical Society, Volume 122, Issue 1, Page 42-68, January 2021., 2021 Abstract We explore the existence and nonlinear stability of boundary spike‐layer solutions of the Keller–Segel system with logarithmic singular sensitivity in the half space, where the physical zero‐flux and Dirichlet boundary conditions are prescribed.
Jose A. Carrillo +2 more
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Sign changing solutions of Poisson's equation
Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 513-536, September 2020., 2020 Abstract Let Ω be an open, possibly unbounded, set in Euclidean space Rm with boundary ∂Ω, let A be a measurable subset of Ω with measure |A| and let γ∈(0,1). We investigate whether the solution vΩ,A,γ of −Δv=γ1Ω∖A−(1−γ)1A with v=0 on ∂Ω changes sign. Bounds are obtained for |A| in terms of geometric characteristics of Ω (bottom of the spectrum of the ...
M. van den Berg, D. Bucur
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Free surface flow over an obstacle. Theoretical study of the fluvial case
Abstract and Applied Analysis, Volume 6, Issue 7, Page 413-429, 2001., 2001 The two‐dimensional stationary flow of a fluid over an obstacle lying on the bottom of a stream is discussed. We take into account the gravity and we neglect the effects of the surface tension. An existence theory for the solution of this problem is established by the implicit function theorem, for small obstacles and Froude numbers in an interval ...
D. Boukari, R. Djouadi, D. Teniou
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On nonstandard potentials in a Stefan problem
International Journal of Stochastic Analysis, Volume 3, Issue 2, Page 153-154, 1990., 1990 We report some results on nonstandard potentials and their application to solution of the Stefan problem.
Igor Malyshev
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Surface integrals approach to solution of some free boundary problems ‐ II
International Journal of Stochastic Analysis, Volume 2, Issue 2, Page 91-100, 1989., 1989 This paper is a continuation of the publication [1] where integral equation techniques were applied to the solution of a generalized Stefan problem. The regularization of the corresponding system of nonlinear integral Volterra equations offered here is quite different from that in [1], hence ‐ several new algorithms and numerical experiments.
Igor Malyshev
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Surface integrals approach to solution of some free boundary problems
International Journal of Stochastic Analysis, Volume 1, Issue 4, Page 305-323, 1988., 1988 Inverse problems in which it is required to determine the coefficients of an equation belong to the important class of ill‐posed problems. Among these, of increasing significance, are problems with free boundaries. They can be found in a wide range of disciplines including medicine, materials engineering, control theory, etc.
Igor Malyshev +3 more
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Lewy-Stampacchia’s inequality for a pseudomonotone parabolic problem
Advances in Nonlinear Analysis, 2019 The main aim of this paper is to extend to the case of a pseudomonotone operator Lewy-Stampacchia’s inequality proposed by F. Donati [7] in the framework of monotone operators. For that, an ad hoc type of perturbation of the operator is proposed.
Guibé Olivier +3 more
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