An integro-differential equation with application in heat flow

Author:
R. C. MacCamy

Journal:
Quart. Appl. Math. **35** (1977), 1-19

MSC:
Primary 80.45; Secondary 35L65

DOI:
https://doi.org/10.1090/qam/452184

MathSciNet review:
452184

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Abstract: The problem

**[1]**Barbu, V.,*Integro-differential equations in Hilbert spaces*, Anal. Stunt, ale Univ. Al. I. Cuza den Iasi**19**, 365-383 (1973) MR**0402443****[2]**Grossman, S. I. and R. K. Miller,*Non-linear Volterra integro-differential systems with kernels*, Journal of Diff. Eqs.**13**, 458-476 (1973)**[3]**Gurtin, M. E. and A. C. Pipkin,*A general theory of heat conduction with finite, wave speeds*, Arch, for Rat. Mech. and Anal.**31**, 113-126 (1968) MR**1553521****[4]**Lax, P. D.,*Development of singularities of solutions of non-linear hyperbolic partial differential equations*, Journal Math. Phys.**5**, 611-613 (1964) MR**0165243****[5]**Levin, J. J. and J. A. Nohel,*Perturbations of a non-linear Volterra equation*, Mich. Math. Journal**12**, 431-447 (1965) MR**0182854****[6]**Londen, S. -O.,*The qualitative behavior of the solutions of a non-linear Volterra equation*, Mich. Math. Journal**18**, 321-338 (1971) MR**0293354****[7]**MacCamy, R. C.,*Stability theorems for a class of functional differential equations*, to appear in SIAM Journal of Appl. Math. MR**0404818****[8]**MacCamy, R. C.,*Remarks on frequency domain methods for Volterra integral equations*, to appear in Journal Math. Anal. and Appl. MR**0423020****[9]**MacCamy, R. C. and J. S. Wong,*Stability theorems for some functional differential equations*, Trans. Amer. Math. Soc.**164**, 1-37 (1972)**[10]**Nohel, J. A. and D. F. Shea,*On the global behavior of a non-linear Volterra equation*, to appear in Advances of Math.**[11]**Nishida, T.,*Global smooth solutions for the second order quasilinear equation with first order dissipation*(preprint).**[12]**Steffans, O. J.,*Nonlinear Volterra integral equations with positive definite kernels*, to appear in Proc. of Amer. Math. Soc.

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Additional Information

DOI:
https://doi.org/10.1090/qam/452184

Article copyright:
© Copyright 1977
American Mathematical Society