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Global existence and blowup of solutions to a free boundary problem for mutualistic model
This article is concerned with a system of semilinear parabolic equations with a free boundary, which arises in a mutualistic ecological model. The...
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The porous medium equation with measure data
We study the existence of solutions to the porous medium equation with a nonnegative, finite Radon measure on the right-hand side. We show that such...
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Heat Trace Asymptotics with Singular Weight Functions II
We study the weighted heat trace asymptotics of an operator of Laplace type with mixed boundary conditions where the weight function exhibits radial...
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Generalizing the Keller–Segel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in the Presence of Attraction and Repulsion Between Competitive Interacting Species
In this paper we extend the famous Keller–Segel model for the chemotactic movement of motile species to some multi-species chemotaxis equations. The...
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On the Volume of the Intersection of Two Independent Wiener Sausages
The expected volume of intersection of two independent Wiener sausages in ℝ m , m ≥ 3, up to time t , and associated to non-polar, compact sets K ...
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Parabolic equations with VMO coefficients in generalized Morrey spaces
In this paper, the authors establish the regularity in generalized Morrey spaces of solutions to parabolic equations with VMO coefficients by means...
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Ricci flow of negatively curved incomplete surfaces
We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete...
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Determination of unknown boundary in the composite materials with Stefan-Boltzmann conditions
The authors consider one specific kind of heat transfer problems in a three-dimensional layered domain, with nonlinear Stefan-Boltzmann conditions on...
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Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces
In (0, T )× Ω , Ω open subset of ℝ n , n ≥2, we consider a parabolic operator P = ∂ t −∇ x δ ( t , x )∇ x , where the (scalar) coefficient δ ( t , x ) is piecewise...
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Parabolic Equations with Partially BMO Coefficients and Boundary Value Problems in Sobolev Spaces with Mixed Norms
Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a 11 ) are measurable in time and...
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Numerical method for the inverse heat transfer problem in composite materials with Stefan-Boltzmann conditions
In this paper, one specific kind of heat transfer problem with nonlinear Stefan-Boltzmann conditions are considered in a three dimensional...
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The Dirichlet problem associated to the relativistic heat equation
We prove existence and uniqueness of entropy solutions for the nonhomogeneous Dirichlet problem associated to the relativistic heat equation.
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Hardy Inequality and Weighted Heat Trace
Upper bounds are obtained for the heat trace weighted by a negative power of the distance to the boundary of an open set D in a complete Riemannian...
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Min–max formulæ for the speeds of pulsating travelling fronts in periodic excitable media
This paper is concerned with some nonlinear propagation phenomena for reaction–advection–diffusion equations in a periodic framework. It deals with...
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Blow-up for doubly degenerate nonlinear parabolic equations
In this paper, we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem of some doubly degenerate nonlinear...
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Carleman estimates for parabolic equations with nonhomogeneous boundary conditions
The authors prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions. On the basis of...