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We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular,...

Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient

Francois Bouchut, Francois James, Simona Mancini (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions are obtained for either the conservative backward problem or the advective forward problem by duality. Specific uniqueness criteria are introduced for the backward conservation equation since weak solutions are not unique. A main point is the introduction of a generalized...

Uniqueness for a boundary identification problem in thermal imaging.

Bryan, Kurt, Caudill, Lester F.jun. (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions.

Zhang, Kewei (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Uniqueness for degenerate elliptic sublinear problems in the absence of dead cores.

Garcia-Melian, Jorge (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Uniqueness for first-order hyperbolic systems - with applications to secnd-order elliptic third-order and Maxwell's equations.

Reinhard Racke (1987)

Journal für die reine und angewandte Mathematik

Uniqueness for positive solutions of $p$ -Laplacian problem in an annulus

Eric Nabana (1999)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Uniqueness for radial Ginzburg-Landau type minimizers.

Lei, Yutian (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Uniqueness for the harmonic map flow from surface to general targets.

Alexandre Freire (1995)

Commentarii mathematici Helvetici

Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities.

K. Gröger, J. Rehberg (1993)

Mathematische Zeitschrift

Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations

Guy Barles, Alessio Porretta (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider a class of stationary viscous Hamilton-Jacobi equations aswhere $λ \geq 0$ , $A (x)$ is a bounded and uniformly elliptic matrix and $H (x, ξ)$ is convex in $ξ$ and grows at most like ${| ξ |}^{q} + f (x)$ , with $1 < q < 2$ and $f \in L^{N / q^{'}} (Ω)$ . Under such growth conditions solutions are in general unbounded, and there is not uniqueness of usual weak solutions. We prove that uniqueness holds in the restricted class of solutions satisfying a suitable energy-type estimate,i.e. ${(1 + | u |)}^{\bar{q} - 1} u \in H_{0}^{1} (Ω)$ , for a certain (optimal) exponent $\bar{q}$ . This completes the recent results in [15],...

Uniqueness in a one-dimensional problem of finding a time-dependent potential.

Dyatlov, G.V. (2001)

Siberian Mathematical Journal

Uniqueness in an inverse problem for an elasticity system.

Bukhgeĭm, A.L., Dyatlov, G.V., Kardakov, V.B., Tantserev, E.V. (2004)

Sibirskij Matematicheskij Zhurnal

Uniqueness in Rough Almost Complex Structures, and Differential Inequalities

Jean-Pierre Rosay (2010)

Annales de l’institut Fourier

The study of $J$ -holomorphic maps leads to the consideration of the inequations $| \frac{\partial u}{\partial \bar{z}} | \leq C | u |$ , and $| \frac{\partial u}{\partial \bar{z}} | \leq ϵ | \frac{\partial u}{\partial z} |$ . The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of $u$ vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class $\frac{1}{2}$ , any $J$ -holomorphic curve that is constant on a non-empty...

Uniqueness of a solution of the Cauchy problem for one-dimensional compressible viscous micropolar fluid model.

Mujaković, Nermina (2006)

Applied Mathematics E-Notes [electronic only]

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