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In this paper, we study the time asymptotic behavior of the solution to an abstract Cauchy problem on Banach spaces without restriction on the initial data. The abstract results are then applied to the study of the time asymptotic behavior of solutions of an one-dimensional transport equation with boundary conditions in $L_{1}$ -space arising in growing cell populations and originally introduced by M. Rotenberg, J. Theoret. Biol. 103 (1983), 181–199.

Traces and fine properties of a $B D$ class of vector fields and applications

Luigi Ambrosio, Gianluca Crippa, Stefania Maniglia (2005)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Traces and the F. and M. Riesz theorem for vector fields

Shiferaw Berhanu, Jorge Hounie (2003)

Annales de l’institut Fourier

This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field $L$ . Applications to the F. and M. Riesz property for vector fields are discussed.

Transport equation and Cauchy problem for $B V$ vector fields and applications

Luigi Ambrosio (2004)

Journées Équations aux dérivées partielles

Transport equations with partially $B V$ velocities

Nicolas Lerner (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove the uniqueness of weak solutions for the Cauchy problem for a class of transport equations whose velocities are partially with bounded variation. Our result deals with the initial value problem $\partial_{t} u + X u = f, u_{|_{t = 0}} = g,$ where $X$ is the vector fieldwith a boundedness condition on the divergence of each vector field $a_{1}, a_{2}$ . This model was studied in the paper [LL] with a $W^{1, 1}$ regularity assumption replacing our $B V$ hypothesis. This settles partly a question raised in the paper [Am]. We examine the details of the argument of...

Travelling graphs for the forced mean curvature motion in an arbitrary space dimension

Régis Monneau, Jean-Michel Roquejoffre, Violaine Roussier-Michon (2013)

Annales scientifiques de l'École Normale Supérieure

We construct travelling wave graphs of the form $z = - c t + φ (x)$ , $φ : x \in ℝ^{N - 1} \mapsto φ (x) \in ℝ$ , $N \geq 2$ , solutions to the $N$ -dimensional forced mean curvature motion $V_{n} = - c_{0} + κ$ ( $c \geq c_{0}$ ) with prescribed asymptotics. For any $1$ -homogeneous function $φ_{\infty}$ , viscosity solution to the eikonal equation $| D φ_{\infty} | = \sqrt{{(c / c_{0})}^{2} - 1}$ , we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by $φ_{\infty}$ . We also describe $φ_{\infty}$ in terms of a probability measure on $§^{N - 2}$ .

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The mixed problem for an infinite system of first order functional differential equations.

The N-Dimensional Cauchy-Riemann equations.

The non-homogeneous Vekua equation. (L'équation non-homogène de Vekua.)

The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation

The problem $\nabla \cdot 𝐯 = f$ and singular integrals on Orlicz spaces

The Rayleigh quotient and dynamic programming.

The reverse Hölder inequality for the solution to $p$ -harmonic type system.

The solution of embedding problems in the framework of GAPs with applications on nonlinear PDEs.

The space of exponentially decreasing entire functions and its application to solvability

The two-dimensional eikonal equation.

The $\bar{\partial}$ -Neumann operator on strongly pseudoconvex domain with piecewise smooth boundary

Time asymptotic description of an abstract Cauchy problem solution and application to transport equation

Traces and fine properties of a $B D$ class of vector fields and applications

Traces and the F. and M. Riesz theorem for vector fields

Transport equation and Cauchy problem for $B V$ vector fields and applications

Transport equations with partially $B V$ velocities

Travelling graphs for the forced mean curvature motion in an arbitrary space dimension

Über die Menge erster Integrale gewisser partieller Differetialgleichungen erster Ordnung

Über ein System partieller Differentialgleichungen und einen zugehörigen Bergman-Operator.

Ueber die Jacobi-Hamilton'sche Integrationsmethode der partiellen Differentialgleichungen erster Ordnung

Currently displaying 321 – 340 of 400