Spagnolo, Sergio; Taglialatela, Giovanni The Cauchy problem for properly hyperbolic equations in one space variable. (English) Zbl 1502.35065 J. Hyperbolic Differ. Equ. 19, No. 3, 439-466 (2022). MSC: 35L30 35A01 35A02 PDF BibTeX XML Cite \textit{S. Spagnolo} and \textit{G. Taglialatela}, J. Hyperbolic Differ. Equ. 19, No. 3, 439--466 (2022; Zbl 1502.35065) Full Text: DOI OpenURL
Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Métivier, Guy On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients. (English) Zbl 1439.35317 Indiana Univ. Math. J. 69, No. 3, 785-836 (2020). MSC: 35L45 35B45 35B65 PDF BibTeX XML Cite \textit{F. Colombini} et al., Indiana Univ. Math. J. 69, No. 3, 785--836 (2020; Zbl 1439.35317) Full Text: DOI arXiv OpenURL
Xiong, Xiangtuan; Zhao, Liping; Hon, Y. C. Stability estimate and the modified regularization method for a Cauchy problem of the fractional diffusion equation. (English) Zbl 1294.65090 J. Comput. Appl. Math. 272, 180-194 (2014). MSC: 65M12 65M15 65M30 35R11 35K05 PDF BibTeX XML Cite \textit{X. Xiong} et al., J. Comput. Appl. Math. 272, 180--194 (2014; Zbl 1294.65090) Full Text: DOI OpenURL
Petrova, Anna G. On the problem of control the composition of material in the binary alloy solidification process. (English) Zbl 1279.35122 J. Inverse Ill-Posed Probl. 18, No. 3, 307-320 (2010). MSC: 35R30 35R37 PDF BibTeX XML Cite \textit{A. G. Petrova}, J. Inverse Ill-Posed Probl. 18, No. 3, 307--320 (2010; Zbl 1279.35122) Full Text: DOI OpenURL
Hayasida, Kazuya On some local property of the shape of interfaces for the porous media equation. (English) Zbl 1173.35564 Math. Nachr. 282, No. 5, 697-712 (2009). MSC: 35K65 35K55 35R25 PDF BibTeX XML Cite \textit{K. Hayasida}, Math. Nachr. 282, No. 5, 697--712 (2009; Zbl 1173.35564) Full Text: DOI OpenURL
Ebert, Marcelo Rempel On the Cauchy problem for \(2\times 2\) weakly hyperbolic systems. (English) Zbl 1122.35066 Osaka J. Math. 42, No. 4, 831-860 (2005). MSC: 35L45 35A05 PDF BibTeX XML Cite \textit{M. R. Ebert}, Osaka J. Math. 42, No. 4, 831--860 (2005; Zbl 1122.35066) OpenURL
Dinh Nho Hào A variational method for a domain identification problem for a parabolic equation. (English) Zbl 1069.35025 Chuong, N. M. (ed.) et al., Abstract and applied analysis. Proceedings of the international conference, Hanoi, Vietnam, August 13–17, 2002. River Edge, NJ: World Scientific (ISBN 981-238-944-X/hbk). 125-138 (2004). MSC: 35K20 35A15 35A35 35N10 PDF BibTeX XML Cite \textit{Dinh Nho Hào}, in: Abstract and applied analysis. Proceedings of the international conference, Hanoi, Vietnam, August 13--17, 2002. River Edge, NJ: World Scientific. 125--138 (2004; Zbl 1069.35025) OpenURL
Sumin, V. I. Stability problem for the existence of global solutions to boundary value control problems and Volterra functional equations. (Russian. English summary) Zbl 1067.49002 Vestn. Nizhegorod. Univ. N. I. Lobachevskogo, Mat. 1, 91-107 (2003). MSC: 49J15 49J20 39B72 PDF BibTeX XML Cite \textit{V. I. Sumin}, Vestn. Nizhegorod. Univ. N. I. Lobachevskogo, Mat. 1, 91--107 (2003; Zbl 1067.49002) OpenURL
Depauw, Nicoals Nonuniqueness of transport by an almost BV vector field. (Non-unicité du transport par un champ de vecteurs presque BV.) (French) Zbl 1063.35054 Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 2002-2003, Exp. No. XIX, 9 p. (2003). Reviewer: Lutz Recke (Berlin) MSC: 35F20 35L60 PDF BibTeX XML Cite \textit{N. Depauw}, Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau 2002--2003, Exp. No. XIX, 9 p. (2003; Zbl 1063.35054) Full Text: Numdam EuDML OpenURL
Tsuji, Mikio Integration and singularities of solutions for nonlinear second order hyperbolic equation. (English) Zbl 1056.35005 Ancona, Vincenzo (ed.) et al., Hyperbolic differential operators and related problems. New York, NY: Marcel Dekker (ISBN 0-8247-0963-2/pbk). Lect. Notes Pure Appl. Math. 233, 109-127 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35A20 PDF BibTeX XML Cite \textit{M. Tsuji}, Lect. Notes Pure Appl. Math. 233, 109--127 (2003; Zbl 1056.35005) OpenURL
Hayasida, Kazuya Unique continuation for fast diffusion. (English) Zbl 1032.35047 Tsukuba J. Math. 27, No. 1, 175-187 (2003). Reviewer: Panagiotis Ch.Tsamatos (Ioannina) MSC: 35B60 35K65 35K15 PDF BibTeX XML Cite \textit{K. Hayasida}, Tsukuba J. Math. 27, No. 1, 175--187 (2003; Zbl 1032.35047) Full Text: DOI OpenURL
Strohmaier, Alexander On the local structure of the Klein-Gordon field on curved spacetimes. (English) Zbl 0980.81044 Lett. Math. Phys. 54, No. 4, 249-261 (2000). MSC: 81T20 81T05 35L05 35L10 34A12 83D05 PDF BibTeX XML Cite \textit{A. Strohmaier}, Lett. Math. Phys. 54, No. 4, 249--261 (2000; Zbl 0980.81044) Full Text: DOI arXiv OpenURL
Izumiya, S.; Sun, W. Z. Geometric study of quasilinear first order partial differential equations. (English) Zbl 0893.35005 Fukuda, T. (ed.) et al., Real analytic and algebraic singularities. Harlow: Longman. Pitman Res. Notes Math. Ser. 381, 150-163 (1998). Reviewer: V.Iftimie (Bucureşti) MSC: 35A30 35A20 35F20 PDF BibTeX XML Cite \textit{S. Izumiya} and \textit{W. Z. Sun}, in: Real analytic and algebraic singularities. Harlow: Longman. 150--163 (1998; Zbl 0893.35005) OpenURL
Pongérard, Patrice A result on global ramification. (Un résultat de ramification globale.) (French) Zbl 0890.35027 C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 8, 863-865 (1997). MSC: 35G10 32A15 PDF BibTeX XML Cite \textit{P. Pongérard}, C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 8, 863--865 (1997; Zbl 0890.35027) Full Text: DOI OpenURL
Hayasida, Kazuya; Yamashiro, Takaaki An ill-posed estimate of positive solutions of a degenerate nonlinear parabolic equation. (English) Zbl 0871.35053 Tokyo J. Math. 19, No. 2, 331-352 (1996). Reviewer: A.Tsutsumi (Osaka) MSC: 35K65 35K55 35R25 PDF BibTeX XML Cite \textit{K. Hayasida} and \textit{T. Yamashiro}, Tokyo J. Math. 19, No. 2, 331--352 (1996; Zbl 0871.35053) Full Text: DOI OpenURL
Hào, Dinh Nho; Reinhardt, H.-J. Recent contributions to linear inverse heat conduction problems. (English) Zbl 0856.35129 J. Inverse Ill-Posed Probl. 4, No. 1, 23-32 (1996). Reviewer: S.Handrock-Meyer (Berlin) MSC: 35R30 35K20 65M30 PDF BibTeX XML Cite \textit{D. N. Hào} and \textit{H. J. Reinhardt}, J. Inverse Ill-Posed Probl. 4, No. 1, 23--32 (1996; Zbl 0856.35129) Full Text: DOI OpenURL
Dinh Nho Hào; Reinhardt, H.-J. Stable numerical solution to linear inverse heat conduction problems by the conjugate gradient method. (English) Zbl 0855.35127 J. Inverse Ill-Posed Probl. 3(1995), No. 6, 447-467 (1996). Reviewer: S.Handrock-Meyer (Berlin) MSC: 35R30 35K20 65M30 PDF BibTeX XML Cite \textit{Dinh Nho Hào} and \textit{H. J. Reinhardt}, J. Inverse Ill-Posed Probl. 3(1995), No. 6, 447--467 (1996; Zbl 0855.35127) Full Text: DOI OpenURL
Dinh Nho Hào; Schneider, A.; Reinhardt, H.-J. Regularization of a non-characteristic Cauchy problem for a parabolic equation. (English) Zbl 0845.35130 Inverse Probl. 11, No. 6, 1247-1263 (1995). Reviewer: S.Handrock-Meyer (Berlin) MSC: 35R25 35K20 65M06 PDF BibTeX XML Cite \textit{Dinh Nho Hào} et al., Inverse Probl. 11, No. 6, 1247--1263 (1995; Zbl 0845.35130) Full Text: DOI OpenURL
Dinh Nho Hào Stability results on a non-characteristic Cauchy problem for a parabolic equation. (English) Zbl 0839.35142 Dang Dinh Ang (ed.) et al., Inverse problems and applications to geophysics, industry, medicine and technology. Proceedings of the international workshop on inverse problems, 17-19 January 1995, HoChiMinh City, Vietnam. HoChiMinh City: Vietnam Mathematical Society, Publ. HoChiMinh City Math. Soc. 2, 71-82 (1995). MSC: 35R30 35K05 65M30 PDF BibTeX XML Cite \textit{Dinh Nho Hào}, in: Inverse problems and applications to geophysics, industry, medicine and technology. Proceedings of the international workshop on inverse problems, 17-19 January 1995, HoChiMinh City, Vietnam. HoChiMinh City: Vietnam Mathematical Society. 71--82 (1995; Zbl 0839.35142) OpenURL
Pettigrew, M. F.; Meredith, D. G. A Laguerre expansion of the Cauchy problem for the diffusion equation. (English) Zbl 0810.35151 Inverse Probl. 10, No. 5, 1165-1183 (1994). MSC: 35R30 35K05 35C10 PDF BibTeX XML Cite \textit{M. F. Pettigrew} and \textit{D. G. Meredith}, Inverse Probl. 10, No. 5, 1165--1183 (1994; Zbl 0810.35151) Full Text: DOI OpenURL
Hào, Dinh Nho A non-characteristic Cauchy problem for linear parabolic equations and related inverse problems. I: Solvability. (English) Zbl 0799.35224 Inverse Probl. 10, No. 2, 295-315 (1994). Reviewer: S.Handrock-Meyer (Berlin) MSC: 35R30 35K10 PDF BibTeX XML Cite \textit{D. N. Hào}, Inverse Probl. 10, No. 2, 295--315 (1994; Zbl 0799.35224) Full Text: DOI OpenURL
Métivier, G. Counterexamples to Hölmgren’s uniqueness for analytic nonlinear Cauchy problems. (English) Zbl 0794.35026 Invent. Math. 112, No. 1, 217-222 (1993). MSC: 35G25 PDF BibTeX XML Cite \textit{G. Métivier}, Invent. Math. 112, No. 1, 217--222 (1993; Zbl 0794.35026) Full Text: DOI EuDML OpenURL
Gourdin, Daniel; Munoz, Enrique Levi conditions for semi linear partial differential systems. (Conditions de Levi pour des systèmes aux dérivées partielles semi- linéaires.) (French. Abridged English version) Zbl 0781.35035 C. R. Acad. Sci., Paris, Sér. I 316, No. 12, 1283-1288 (1993). MSC: 35L45 35B65 PDF BibTeX XML Cite \textit{D. Gourdin} and \textit{E. Munoz}, C. R. Acad. Sci., Paris, Sér. I 316, No. 12, 1283--1288 (1993; Zbl 0781.35035) OpenURL
Leichtnam, Éric The ramified semilinear Cauchy problem of second order. (Le problème de Cauchy ramifié semi-linéaires d’ordre deux.) (French) Zbl 0804.35006 Ann. Sci. Éc. Norm. Supér. (4) 24, No. 2, 189-214 (1991). Reviewer: G.Zampieri (Padova) MSC: 35A20 35S05 PDF BibTeX XML Cite \textit{É. Leichtnam}, Ann. Sci. Éc. Norm. Supér. (4) 24, No. 2, 189--214 (1991; Zbl 0804.35006) Full Text: DOI Numdam EuDML OpenURL
Gourdin, Daniel Problème de Cauchy faiblement hyperbolique. II. (Weakly hyperbolic Cauchy problem. II). (French) Zbl 0658.35057 J. Math. Kyoto Univ. 27, 27-45 (1987). Reviewer: M.Kisielewicz MSC: 35L15 35L45 35A05 PDF BibTeX XML Cite \textit{D. Gourdin}, J. Math. Kyoto Univ. 27, 27--45 (1987; Zbl 0658.35057) Full Text: DOI OpenURL
Eldén, Lars Modified equations for approximating the solution of a Cauchy problem for the heat equation. (English) Zbl 0629.65104 Inverse and ill-posed problems, Alpine-U.S. Semin. St. Wolfgang/Austria 1986, Notes Rep. Math. Sci. Eng. 4, 345-350 (1987). MSC: 65M25 65M15 35K05 35R25 PDF BibTeX XML OpenURL
Igari, Katsuju On the Cauchy-Kowalewski theorem for characteristic initial surfaces. (English) Zbl 0627.35002 Proc. Japan Acad., Ser. A 63, 7-9 (1987). Reviewer: J.Jaenicke MSC: 35A10 35G05 PDF BibTeX XML Cite \textit{K. Igari}, Proc. Japan Acad., Ser. A 63, 7--9 (1987; Zbl 0627.35002) Full Text: DOI OpenURL
Persson, Jan Quasianalytic classes, Holmgren’s uniqueness theorem, Hamilton-Jacobi equations and the inverse function theorem. (English) Zbl 0631.35003 Current topics in partial differential equations, Pap. dedic. S. Mizohata Occas. 60th Birthday, 27-53 (1986). Reviewer: R.Salvi MSC: 35A20 35A05 PDF BibTeX XML OpenURL
Saint Raymond, Xavier Uniqueness for the linear Cauchy problems of first order. (L’unicité pour les problèmes de Cauchy linéaires du premier ordre.) (French) Zbl 0625.35009 Enseign. Math., II. Sér. 32, 1-55 (1986). Reviewer: Gheorghe Gussi (Bucureşti) MSC: 35F10 35A02 PDF BibTeX XML Cite \textit{X. Saint Raymond}, Enseign. Math. (2) 32, 1--55 (1986; Zbl 0625.35009) Full Text: DOI OpenURL
Groothuizen, R. J. P. Mixed elliptic-hyperbolic partial differential operators: a case-study in Fourier integral operators. (English) Zbl 0566.35072 CWI Tracts, 16. Centrum voor Wiskunde en Informatica. Amsterdam: Mathematisch Centrum. III, 147 p. Dfl. 21.40 (1985). Reviewer: M.Schneider MSC: 35M99 35-02 42A38 35A08 35B65 35S10 35S15 PDF BibTeX XML OpenURL
Nakane, Shizuo Non-uniqueness in the Cauchy problem for partial differential operators with multiple characteristics. I. (English) Zbl 0559.35001 Commun. Partial Differ. Equations 9, 63-106 (1984). Reviewer: T.Rassias MSC: 35A10 35A30 35A05 PDF BibTeX XML Cite \textit{S. Nakane}, Commun. Partial Differ. Equations 9, 63--106 (1984; Zbl 0559.35001) Full Text: DOI OpenURL
Lerner, N.; Robbiano, L. Unicité de Cauchy pour des opérateurs de type principal à coefficients \(C^{\infty}\). (French) Zbl 0551.35016 Sémin. Goulaouic-Meyer-Schwartz 1983-1984, Équat. dériv. part., Exposé No. 9, 9 p. (1984). Reviewer: Yu.V.Egorov MSC: 35G10 PDF BibTeX XML Full Text: Numdam EuDML OpenURL
Nakane, Shizuo Uniqueness and non-uniqueness in the Cauchy problem for a class of operators of degenerate type. II. (English) Zbl 0577.35067 Proc. Japan Acad., Ser. A 59, 318-320 (1983). MSC: 35L15 35A05 PDF BibTeX XML Cite \textit{S. Nakane}, Proc. Japan Acad., Ser. A 59, 318--320 (1983; Zbl 0577.35067) Full Text: DOI OpenURL
Nakane, Shizuo Non-uniqueness in the Cauchy problem for partial differential operators with multiple characteristics. II. (English) Zbl 0577.35020 Proc. Japan Acad., Ser. A 59, 361-363 (1983). MSC: 35G10 35A05 PDF BibTeX XML Cite \textit{S. Nakane}, Proc. Japan Acad., Ser. A 59, 361--363 (1983; Zbl 0577.35020) Full Text: DOI OpenURL
Knabner, Peter Regularizing the Cauchy problem for the heat equation by sign restrictions. (English) Zbl 0508.65047 Improperly posed problems and their numerical treatment, Conf. Oberwolfach 1982, ISNM 63, 165-177 (1983). MSC: 65M60 65M30 35K05 PDF BibTeX XML OpenURL
Gourdin, Daniel Problème de Cauchy faiblement hyperbolique. (French) Zbl 0523.35069 Bull. Sci. Math., II. Ser. 106, 259-272 (1982). MSC: 35L15 35L45 PDF BibTeX XML Cite \textit{D. Gourdin}, Bull. Sci. Math., II. Sér. 106, 259--272 (1982; Zbl 0523.35069) OpenURL
Kobayashi, Takao Elementary solutions and propagation of singularities for hyperbolic operators with involutive characteristics. (English) Zbl 0507.35054 Commun. Partial Differ. Equations 7, 1189-1216 (1982). MSC: 35L30 35L67 35A07 35A30 PDF BibTeX XML Cite \textit{T. Kobayashi}, Commun. Partial Differ. Equations 7, 1189--1216 (1982; Zbl 0507.35054) Full Text: DOI OpenURL
Wagschal, Claude Problème de Cauchy à caractéristiques multiples de multiplicité variable. (French) Zbl 0506.35018 C. R. Acad. Sci., Paris, Sér. I 293, 641-644 (1981). MSC: 35F10 35A30 35C05 PDF BibTeX XML Cite \textit{C. Wagschal}, C. R. Acad. Sci., Paris, Sér. I 293, 641--644 (1981; Zbl 0506.35018) OpenURL
Urabe, Jiichiroh On Hamada’s theorem for a certain operator with double characteristics. (English) Zbl 0503.35061 J. Math. Kyoto Univ. 21, 517-535 (1981). MSC: 35M99 35L80 35A07 PDF BibTeX XML Cite \textit{J. Urabe}, J. Math. Kyoto Univ. 21, 517--535 (1981; Zbl 0503.35061) Full Text: DOI OpenURL
McCoy, Peter A. Bernstein theorems for a parabolic equation in one space variable. (English) Zbl 0507.41007 Approximation theory III, Proc. Conf. Hon. G. G. Lorentz, Austin/Tex. 1980, 643-646 (1980). MSC: 41A10 41A50 34A25 34A12 PDF BibTeX XML OpenURL
Schiltz, D.; Vaillant, J.; Wagschal, C. Problème de Cauchy ramifie à caractéristiques multiples en involution. (French) Zbl 0474.35059 Equations aux derivees partielles hyperboliques et holomorphes, Semin. Paris, Annee 1979-1980, Expose No. 10, 5 p. (1980). MSC: 35L25 PDF BibTeX XML OpenURL
Hansen, Sönke Uniqueness of the Cauchy problem for convolution equations. (English) Zbl 0423.35006 J. Reine Angew. Math. 317, 1-15 (1980). MSC: 35A30 35A05 46F10 PDF BibTeX XML Cite \textit{S. Hansen}, J. Reine Angew. Math. 317, 1--15 (1980; Zbl 0423.35006) Full Text: DOI EuDML Link OpenURL
Hoffmann, K.-H.; Knabner, P. Freie Randwertprobleme. (German) Zbl 0464.35098 Approximation in Theorie und Praxis, Symp. Siegen 1979, 25-56 (1979). MSC: 35R35 35R30 35K10 35R25 PDF BibTeX XML OpenURL
Rea, Claudio Approximated Cauchy problem for linear, first order, overdetermined systems. (English) Zbl 0445.35030 Ann. Mat. Pura Appl., IV. Ser. 122, 383-397 (1979). MSC: 35F99 35N10 35J99 35N99 PDF BibTeX XML Cite \textit{C. Rea}, Ann. Mat. Pura Appl. (4) 122, 383--397 (1979; Zbl 0445.35030) Full Text: DOI OpenURL
Lascar, Bernard Théoreme de Cauchy-Kovalevsky et théorème d’unicité d’Holmgren pour des fonctions analytiques d’une infinite de variables. (French) Zbl 0438.35005 Advances in Holomorphy, Proc. Semin., Rio de Janeiro 1977, North-Holland Math. Stud. 34, 485-508 (1979). MSC: 35A10 35A08 35R15 35B65 46G20 PDF BibTeX XML OpenURL
Oganesyan, G. R. Mixed problems for weakly hyperbolic equations with two independent variables. (Russian) Zbl 0426.35011 Izv. Akad. Nauk Arm. SSR, Mat. 14, 369-390 (1979). MSC: 35A30 35L99 PDF BibTeX XML Cite \textit{G. R. Oganesyan}, Izv. Akad. Nauk Arm. SSR, Mat. 14, 369--390 (1979; Zbl 0426.35011) OpenURL
Urabe, Jiichiroh On the theorem of Hamada for a linear second order equation with variable multiplicities. (English) Zbl 0413.35006 J. Math. Kyoto Univ. 19, 153-169 (1979). MSC: 35A20 35M99 35A30 PDF BibTeX XML Cite \textit{J. Urabe}, J. Math. Kyoto Univ. 19, 153--169 (1979; Zbl 0413.35006) Full Text: DOI OpenURL
Zuily, C. Unicité du problème de Cauchy pour une classe d’opérateurs différentiels à caractéristiques de multiplicité constante. (French) Zbl 0409.35001 Journ. Équ. Dériv. Partielles, Saint-Cast 1979, Exp. No. 12, 5 p. (1979). MSC: 35A05 35B45 PDF BibTeX XML Full Text: Numdam OpenURL
Nishitani, Tatsuo On the Lax-Mizohata theorem in the analytic and Gevrey classes. (English) Zbl 0442.35025 Proc. Japan Acad., Ser. A 53, 88-90 (1977). MSC: 35G10 35A99 35L30 35S10 PDF BibTeX XML Cite \textit{T. Nishitani}, Proc. Japan Acad., Ser. A 53, 88--90 (1977; Zbl 0442.35025) Full Text: DOI OpenURL
MacKichan, B. The Cauchy problem for overdetermined systems of partial differential equations. (English) Zbl 0412.35020 Renc. Anal. compl. plus. Var. Syst. surdeterm., Conf. Montreal 1974, 167-180 (1975). MSC: 35F15 58J45 58J10 55U99 PDF BibTeX XML OpenURL