References
- Alinhac , S . 1995 . Blowup for Nonlinear Hyperbolic Equations , Boston : Birkhauser .
- Hörmander , L . 1997 . Lectures on Nonlinear Hyperbolic Differential Equations , Paris : Springer .
- John , F . 1974 . Formation of singularities in one dimensional nonlinear wave propagation . Commun. Pure Appl. Math. , 27 : 317 – 405 .
- Popivanov , P . 2006 . Geometrical Methods for Solving of Fully Nonlinear Partial Differential Equations , Vol. 2 , Sofia , , Bulgaria : Mathematics and its Applications .
- Popivanov , P . 2003 . “ Nonlinear PDE, Singularities, propagation, applications ” . In Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations , Edited by: Albeverio , S , Demuth , M , Schrohe , E and Schulze , B-W . Vol. 145 , 1 – 94 . Basel : Advances in Partial Differential Equations, Birkhuser .
- Ëltysheva , NA . 1988 . On qualitative properties of solutions of some hyperbolic system on the plane . Mat. Sb. , 134 ( 2 ) : 186 – 209 .
- Lavrent'ev , MM Jr and Lyul'ko , NA . 1997 . Increasing smoothness of solutions to some hyperbolic problems . Sib. Math. J. , 38 ( 1 ) : 92 – 105 .
- Oberguggenberger , M . 1986 . Propagation of singularities for semilinear hyperbolic initial-boundary value problems in one space dimension . J. Differ. Eqns , 61 : 1 – 39 .
- Rauch , J and Reed , M . 1981 . Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: Creation and propagation . Commun. Math. Phys. , 81 : 203 – 207 .
- Kmit , I . 2007 . A distributional solution to a hyperbolic problem arising in population dynamics . Electron. J. Differ. Eqns , 2007 ( 132 ) : 1 – 23 .
- Travers , KE . 1997 . Semilinear hyperbolic systems in one space dimension with strongly singular initial data . Electron. J. Differ. Eqns , 1997 ( 14 ) : 1 – 11 .
- Kmit , I . 2008 . Classical solvability of nonlinear initial-boundary problems for first-order hyperbolic systems . Int. J. Dyn. Syst. Differ. Eqns , 1 ( 3 ) : 191 – 195 .
- Oberguggenberger , M . 1992 . Multiplication of Distributions and Applications to Partial Differential Equations , Pitman Research Notes in Mathematics, Vol. 259 Harlow : Longman Scientific & Technical .
- Lyul'ko , NA . 2004 . Increasing the smoothness of solutions of a mixed problem for the wave equation in the plane . Mat. Fiz. Anal. Geom. , 11 ( 2 ) : 169 – 176 .
- Akramov , TA . 1998 . On the behaviour of solutions to a certain hyperbolic problem . Sib. Math. J. , 39 ( 1 ) : 1 – 17 .
- Hillen , T and Hadeler , KP . 2005 . “ Hyperbolic systems and transport equations in mathematical biology ” . In Analysis and Numerics for Conservation Laws , Edited by: Warnecke , G . 257 – 279 . Berlin : Springer .
- Akramov , TA , Belonosov , VS , Zelenyak , TI , Lavrentev , MM Jr , Slinko , MG and Sheplev , VS . 2000 . Mathematical foundations of modeling of catalytic processes: A review . Theor. Found. Chem. Eng. , 34 ( 3 ) : 295 – 306 .
- Slinko , MG . 2007 . History of the development of mathematical modeling of catalytic processes and reactors . Theor. Found. Chem. Eng. , 41 ( 1 ) : 13 – 29 .
- Zelenyak , TI . 1966 . On stationary solutions of mixed problems relating to the study of certain chemical processes . Differ. Eqns , 2 : 98 – 102 .
- Zelenyak , TI . 1967 . The stability of solutions of mixed problems for a particular quasi- linear equation . Differ. Eqns , 3 : 9 – 13 .
- Lichtner , M , Radziunas , M and Recke , L . 2007 . Well-posedness, smooth dependence and center manifold reduction for a semilinear hyperbolic system from laser dynamics . Math. Methods Appl. Sci. , 30 : 931 – 960 .
- Radziunas , M . 2006 . Numerical bifurcation analysis of traveling wave model of multisection semiconductor lasers . Physica D , 213 : 575 – 613 .
- Radziunas , M and Wünsche , H-J . 2005 . “ Dynamics of multisection DFB semiconductor lasers: Traveling wave and mode approximation models ” . In Optoelectronic Devices – Advanced Simulation and Analysis , Edited by: Piprek , J . 121 – 150 . USA : Springer .