Darko Mitrović

Singular solutions of a fully nonlinear 2 × 2 system of conservation laws

Existence and admissibility of δ-shock solutions is discussed for the non-convex strictly hyper- bolic system of equations ∂tu + ∂x( 1 (u 2 + v 2 )) = 0, ∂tv + ∂x(v(u − 1)) = 0. The system is fully nonlinear, i.e. it is nonlinear with respect to both unknowns, and it does not admit the classical Lax-admissible solution for certain Riemann problems. By introducing complex-valued cor- rections in the framework of the weak asymptotic method, we show that a compressive δ-shock solution resolves such Riemann problems. By letting the approximation parameter tend to zero, the corrections become real valued, and the solutions can be seen to fit into the framework of weak singular solutions defined by Danilov and Shelkovich. Indeed, in this context, we can show that every 2 × 2 system of conservation laws admits δ-shock solutions.

STRONG TRACES FOR AVERAGED SOLUTIONS OF HETEROGENEOUS ULTRA-PARABOLIC TRANSPORT EQUATIONS

We prove that if traceability conditions are fulfilled then a weak solution

H-Distributions: An Extension of H-Measures to an L p -L q Setting

h\in L^\infty(\R^+\times\R^d\times \R)

Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function

to {the ultra-parabolic transport equation} \begin{equation*} \pa_t h + \Div_x \left(F(t,x,\lambda)h\right)=\sum\limits_{i,j=1}^k\pa^2_{x_i x_j}\left(b_{ij}(t,x,\lambda) h\right)+\pa_\lambda \gamma(t,x,\lambda), \end{equation*} is such that for every

Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws

\rho\in C^1_c(\R)

Two-Phase Nonturbulent Flow with Applications

, the velocity averaged quantity

Averaged Control for Fractional ODEs and Fractional Diffusion Equations

\int_{\R}h(t,x,\lambda)

-Distributions: An Extension of -Measures to an Setting

\rho(\lambda)d\lambda

H-Distributions: An Extension ofH-Measures to anLp-LqSetting

admits the strong