[1]

Almog Y., Helffer B. (2015) On the spectrum of nonselfadjoint Schrödinger operators with compact resolvent. Comm. PDE 40: 14411466.

[2]

H. Amann, Linear and Quasilinear Parabolic Problems. Vol. I, Abstract Linear Theory, Monographs in Mathematics, vol. 89, Birkhäuser Boston, Inc., Boston, MA, 1995.
10.1007/9783034892216
MR1345385

[3]

W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vectorvalued Laplace Transforms and Cauchy Problems, 2^{nd} ed., Monographs in Mathematics, vol. 96, Birkhäuser/Springer Basel AG, Basel, 2011.
10.1007/9783034800877
MR2798103

[4]

Christensen A.E., Johnsen J. (2018) On parabolic final value problems and wellposedness. C. R. Acad. Sci. Paris, Ser. I 356: 301305.

[5]

Christensen A.E., Johnsen J. (2018) Final value problems for parabolic differential equations and their wellposedness. Axioms 7: 31.

[6]

R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953.
MR0065391

[7]

E. B. Davies, Oneparameter Semigroups, London Mathematical Society Monographs, vol. 15,
Academic Press, Inc., LondonNew York, 1980.
MR591851

[8]

Eldén L. (1987) Approximations for a Cauchy problem for the heat equation. Inverse Problems 3: 263273.

[9]

L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, second ed., American Mathematical Society, Providence, RI, 2010.
10.1090/gsm/019
MR2597943

[10]

Grebenkov D.S., Helffer B., Henry R. (2017) The complex Airy operator on the line with a semipermeable barrier. SIAM J. Math. Anal. 49: 18441894.

[11]

Grebenkov D. S., Helffer B. (2018) On the spectral properties of the Bloch–Torrey operator in two dimensions. SIAM J. Math. Anal. 50: 622676.

[12]

G. Grubb, Distributions and Operators, Graduate Texts in Mathematics, vol. 252, Springer, New York, 2009.
MR2453959

[13]

Grubb G., Solonnikov V. A. (1990) Solution of parabolic pseudodifferential initialboundary value problems. J. Differential Equations 87: 256304.

[14]

B. Helffer, Spectral Theory and Its Applications, Cambridge Studies in Advanced Mathematics, vol. 139, Cambridge University Press, Cambridge, 2013.
MR3027462

[15]

Herbst I. W. (1979) Dilation analyticity in constant electric field. I. The two body problem. Comm. Math. Phys. 64: 279298.

[16]

L. Hörmander, The Analysis of Linear Partial Differential Operators I, Grundlehren der mathematischen Wissenschaften, Springer Verlag, Berlin, 1983.
10.1007/9783642967504
MR717035

[17]

L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques & Applications, vol. 26, Springer Verlag, Berlin, 1997.
MR1466700

[18]

Janas J. (1994) On unbounded hyponormal operators Ⅲ. Studia Mathematica 112: 7582.

[19]

John F. (1955) Numerical solution of the equation of heat conduction for preceding times. Ann. Mat. Pura Appl. (4) 40: 129142.

[20]

Johnsen J. (2018) Characterization of logconvex decay in nonselfadjoint dynamics. Elec. Res. Ann. Math. 25: 7286.

[21]

J. Johnsen, A class of wellposed parabolic final value problems, Appl. Num. Harm. Ana., Birkhäuser (to appear). arXiv: 1904.05190.

[22]

O. A. Ladyzenskaya, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Translations of mathematical monographs, vol. 23, Amer. Math. Soc., 1968.
MR0241822

[23]

Lions J.L., Malgrange B. (1960) Sur l'unicité rétrograde dans les problèmes mixtes parabolic. Math. Scand. 8: 227286.

[24]

J.L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problems and Applications. Vol. I, SpringerVerlag, New YorkHeidelberg, 1972, Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181.
MR0350177

[25]

Miranker W. L. (1961) A well posed problem for the backward heat equation. Proc. Amer. Math. Soc. 12: 243247.

[26]

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44, SpringerVerlag, New York, 1983.
10.1007/9781461255611
MR710486

[27]

J. Rauch, Partial Differential Equations, Springer, 1991.
10.1007/9781461209539
MR1223093

[28]

L. Schwartz, Théorie Des Distributions, revised and enlarged ed., Hermann, Paris, 1966.
MR0209834

[29]

Showalter R. E. (1974) The final value problem for evolution equations. J. Math. Anal. Appl. 47: 563572.

[30]

H. Tanabe, Equations of Evolution, Monographs and Studies in Mathematics, vol. 6, Pitman, Boston, Mass., 1979.
MR533824

[31]

R. Temam, Navier–Stokes Equations, Theory and Numerical Analysis, Elsevier Science Publishers B.V., Amsterdam, 1984.
MR769654

[32]

K. Yosida, Functional Analysis, 6^{th} ed., SpringerVerlag, BerlinNew York, 1980.
MR617913
