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We revisit the existence problem for shock profiles in quasilinear relaxation systems in the case that the velocity is a characteristic mode, implying that the profile ODE is degenerate. Our result states existence, with sharp rates of decay and distance from the Chapman–Enskog approximation, of small-amplitude quasilinear relaxation shocks. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman–Enskog expansion and the macro–micro...

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Evanescent solutions for linear ordinary differential equations.

Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem.

Existence and multiplicity results for singular $φ$ -Laplacian BVPs on the positive half-line.

Existence and uniqueness of positive solutions for a BVP with a $p$ -Laplacian on the half-line.

Existence and uniqueness of very singular solution of a degenerate parabolic equation with nonlinear convection.

Existence of multiple positive solutions for third-order boundary-value problem on the half-line with dependence on the first order derivative.

Existence of positive solution for second-order impulsive boundary value problems on infinity intervals.

Existence of positive solutions for boundary value problems of second-order nonlinear differential equations on the half line.

Existence of quasilinear relaxation shock profiles in systems with characteristic velocities

Existence of solutions for second-order differential equations and systems on infinite intervals.

Existence of solutions to second order ordinary differential equations having finite limits at $\pm$ infinity.

Existence of three positive solutions for $m$ -point discrete boundary value problems with $p$ -Laplacian.

Existence problems for homoclinic solutions.

Existence problems for $ω$ -closed orbits.

Currently displaying 1 – 14 of 14