Solvability of Cauchy Problem for One System of First Order Quasilinear Differential Equations

		ISSN 1683-3414 (Print) • ISSN 1814-0807 (Online)

		Log in

Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system’s guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/t8227-2101-5573-p Solvability of Cauchy Problem for One System of First Order Quasilinear Differential Equations Dontsova, M. V. Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 3. Abstract: We consider the Cauchy problem for a system of first-order quasilinear differential equations. The solvability of the problem is investigated in the initial coordinates using the additional argument method. Sufficient conditions for the existence and uniqueness of a local solution which has the same smoothness in the independent variable as the initial functions of the Cauchy problem are determined. An existence and uniqueness theorem of a local solution is proved. Sufficient conditions for the existence and uniqueness of a global solution are determined. The proof of the global solvability relies upon global estimates. Keywords: method of an additional argument, Cauchy problem, first-order partial differential equation Language: Russian Download the full text For citation: Dontsova, M. V. Solvability of Cauchy Problem for One System of First Order Quasilinear Differential Equations, Vladikavkaz Math. J., 2021, vol. 23, no. 3, pp. 64-79. DOI 10.46698/t8227-2101-5573-p + References 1. Dontsova, M. V. Solvability of the Cauchy Problem for a Quasilinear System in Original Coordinates, Journal of Mathematical Sciences, 2020, vol. 249, no. 6, pp. 918-928. 2. Dontsova, M. V. Solvability of Cauchy Problem for a System of First Order Quasilinear Equations with Right-Hand Sides \(f_1=a_2u(t,x) + b_2(t)v(t,x)\), \(f_2=g_2v(t,x)\), Ufa Mathematical Journal, 2019, vol. 11, no. 1, pp. 27-41. DOI: 10.13108/2019-11-1-27. 3. Dontsova, M. V. Sufficient Conditions of a Nonlocal Solvability for a System of two Quasilinear Equations of the First Order with Constant Terms, Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2020, vol. 55, pp. 60-78 (in Russian). DOI: 10.35634/2226-3594-2020-55-05. 4. Dontsova, M. V. The Nonlocal Solvability for a System with Constant Terms for the Case of Positive Coefficients, Zhurnal Srednevolzhskogo matematicheskogo obshchestva [Journal of the Middle Volga Mathematical Society], 2017, vol. 19, no. 4, pp. 23-32 (in Russian). DOI: 10.15507/2079-6900.19.201704.23-32. 5. Alekseenko, S. N., Dontsova, M. V., Pelinovsky, P. E. Global Solutions to the Shallow-Water System with a Method of an Additional Argument, Applicable Analysis, 2017, vol. 96, no. 9, pp. 1444-1465. DOI: 10.1080/00036811.2016.1208817. 6. Imanaliev, M. I., Alekseenko, S. N. To the Question of the Existence of a Smooth Bounded Solution for a system of Two First-Order Nonlinear Partial, Differential Equations, Doklady RAN [Doklady Mathematics], 2001, vol. 379, no. 1, pp. 16-21 (in Russian). 7. Dontsova, M. V. Nonlocal Solvability Conditions for Cauchy Problem for a System of First Order Partial Differential Equations with Special Right-Hand Sides, Ufa Mathematical Journal, 2014, vol. 6, no. 4, pp. 68-80. DOI: 10.13108/2014-6-4-68. ← Contents of issue


	\| Home \| Editorial board \| Publication ethics \| Peer review guidelines \| Latest issue \| All issues \| Rules for authors \| Online submission system’s guidelines \| Submit manuscript \|
	© 1999-2023 Южный математический институт